รายการปร, นธ, ของฟ, งก, นตร, โกณม, อไปน, เป, นรายการปร, นธ, งก, นปฏ, ยาน, นธ, ของฟ, งก, นตร, โกณม, โดยท, วไป, าฟ, งก, displaystyle, เป, นฟ, งก, นตร, โกณม, ใด, และ, displaystyle, เป, นอน, นธ, ของม, แล, displaystyle, frac, ในท, กส, ตร, กำหนดให, าคงต, เป, นจำนวนท. txipniepnraykarpriphnth fngkchnptiyanuphnth khxngfngkchntrioknmiti odythwip thafngkchn sin x displaystyle sin x epnfngkchntrioknmitiid aela cos x displaystyle cos x epnxnuphnthkhxngmn aelw a cos n x d x a n sin n x C displaystyle int a cos nx dx frac a n sin nx C inthuksutr kahndih khakhngtw a epncanwnthiimichsuny aela C epnkhakhngtwkhxngkarhapriphnth enuxha 1 priphthththiekiywkhxngechphaaisn 2 priphthththiekiywkhxngechphaaokhisn 3 priphthththiekiywkhxngechphaaaethnecnt 4 priphthththiekiywkhxngechphaaesaekhnt 5 priphthththiekiywkhxngechphaaokhesaekhnt 6 priphthththiekiywkhxngechphaaokhaethnecnt 7 priphthththiekiywkhxngthngisnaelaokhisn 8 priphthththiekiywkhxngthngisnaelaaethnecnt 9 priphthththiekiywkhxngthngokhisnaelaaethnecnt 10 priphthththiekiywkhxngthngisnaelaokhaethnecnt 11 priphthththiekiywkhxngthngokhisnaelaokhaethnecnt 12 priphthththiekiywkhxngthngesaekhntaelaaethnecnt 13 priphthththiekiywkhxngthngokhesaekhntaelaokhaethnecntpriphthththiekiywkhxngechphaaisn aekikh sin a x d x 1 a cos a x C displaystyle int sin ax dx frac 1 a cos ax C sin 2 a x d x x 2 1 4 a sin 2 a x C x 2 1 2 a sin a x cos a x C displaystyle int sin 2 ax dx frac x 2 frac 1 4a sin 2ax C frac x 2 frac 1 2a sin ax cos ax C sin 3 a x d x cos 3 a x 12 a 3 cos a x 4 a C displaystyle int sin 3 ax dx frac cos 3ax 12a frac 3 cos ax 4a C x sin 2 a x d x x 2 4 x 4 a sin 2 a x 1 8 a 2 cos 2 a x C displaystyle int x sin 2 ax dx frac x 2 4 frac x 4a sin 2ax frac 1 8a 2 cos 2ax C x 2 sin 2 a x d x x 3 6 x 2 4 a 1 8 a 3 sin 2 a x x 4 a 2 cos 2 a x C displaystyle int x 2 sin 2 ax dx frac x 3 6 left frac x 2 4a frac 1 8a 3 right sin 2ax frac x 4a 2 cos 2ax C sin b 1 x sin b 2 x d x sin b 2 b 1 x 2 b 2 b 1 sin b 1 b 2 x 2 b 1 b 2 C sahrb b 1 b 2 displaystyle int sin b 1 x sin b 2 x dx frac sin b 2 b 1 x 2 b 2 b 1 frac sin b 1 b 2 x 2 b 1 b 2 C qquad mbox sahrb b 1 neq b 2 mbox sin n a x d x sin n 1 a x cos a x n a n 1 n sin n 2 a x d x sahrb n gt 0 displaystyle int sin n ax dx frac sin n 1 ax cos ax na frac n 1 n int sin n 2 ax dx qquad mbox sahrb n gt 0 mbox d x sin a x 1 a ln csc a x cot a x C displaystyle int frac dx sin ax frac 1 a ln left csc ax cot ax right C d x sin n a x cos a x a 1 n sin n 1 a x n 2 n 1 d x sin n 2 a x sahrb n gt 1 displaystyle int frac dx sin n ax frac cos ax a 1 n sin n 1 ax frac n 2 n 1 int frac dx sin n 2 ax qquad mbox sahrb n gt 1 mbox x sin a x d x sin a x a 2 x cos a x a C displaystyle int x sin ax dx frac sin ax a 2 frac x cos ax a C x n sin a x d x x n a cos a x n a x n 1 cos a x d x k 0 2 k n 1 k 1 x n 2 k a 1 2 k n n 2 k cos a x k 0 2 k 1 n 1 k x n 1 2 k a 2 2 k n n 2 k 1 sin a x k 0 n x n k a 1 k n n k cos a x k p 2 sahrb n gt 0 displaystyle begin aligned int x n sin ax dx amp frac x n a cos ax frac n a int x n 1 cos ax dx amp sum k 0 2k leq n 1 k 1 frac x n 2k a 1 2k frac n n 2k cos ax sum k 0 2k 1 leq n 1 k frac x n 1 2k a 2 2k frac n n 2k 1 sin ax amp sum k 0 n frac x n k a 1 k frac n n k cos left ax k frac pi 2 right qquad mbox sahrb n gt 0 mbox end aligned sin a x x d x n 0 1 n a x 2 n 1 2 n 1 2 n 1 C displaystyle int frac sin ax x dx sum n 0 infty 1 n frac ax 2n 1 2n 1 cdot 2n 1 C sin a x x n d x sin a x n 1 x n 1 a n 1 cos a x x n 1 d x displaystyle int frac sin ax x n dx frac sin ax n 1 x n 1 frac a n 1 int frac cos ax x n 1 dx d x 1 sin a x 1 a tan a x 2 p 4 C displaystyle int frac dx 1 pm sin ax frac 1 a tan left frac ax 2 mp frac pi 4 right C x d x 1 sin a x x a tan a x 2 p 4 2 a 2 ln cos a x 2 p 4 C displaystyle int frac x dx 1 sin ax frac x a tan left frac ax 2 frac pi 4 right frac 2 a 2 ln left cos left frac ax 2 frac pi 4 right right C x d x 1 sin a x x a cot p 4 a x 2 2 a 2 ln sin p 4 a x 2 C displaystyle int frac x dx 1 sin ax frac x a cot left frac pi 4 frac ax 2 right frac 2 a 2 ln left sin left frac pi 4 frac ax 2 right right C sin a x d x 1 sin a x x 1 a tan p 4 a x 2 C displaystyle int frac sin ax dx 1 pm sin ax pm x frac 1 a tan left frac pi 4 mp frac ax 2 right C priphthththiekiywkhxngechphaaokhisn aekikh cos a x d x 1 a sin a x C displaystyle int cos ax dx frac 1 a sin ax C cos 2 a x d x x 2 1 4 a sin 2 a x C x 2 1 2 a sin a x cos a x C displaystyle int cos 2 ax dx frac x 2 frac 1 4a sin 2ax C frac x 2 frac 1 2a sin ax cos ax C cos n a x d x cos n 1 a x sin a x n a n 1 n cos n 2 a x d x sahrb n gt 0 displaystyle int cos n ax dx frac cos n 1 ax sin ax na frac n 1 n int cos n 2 ax dx qquad mbox sahrb n gt 0 mbox x cos a x d x cos a x a 2 x sin a x a C displaystyle int x cos ax dx frac cos ax a 2 frac x sin ax a C x 2 cos 2 a x d x x 3 6 x 2 4 a 1 8 a 3 sin 2 a x x 4 a 2 cos 2 a x C displaystyle int x 2 cos 2 ax dx frac x 3 6 left frac x 2 4a frac 1 8a 3 right sin 2ax frac x 4a 2 cos 2ax C x n cos a x d x x n sin a x a n a x n 1 sin a x d x k 0 2 k 1 n 1 k x n 2 k 1 a 2 2 k n n 2 k 1 cos a x k 0 2 k n 1 k x n 2 k a 1 2 k n n 2 k sin a x k 0 n 1 k 2 x n k a 1 k n n k cos a x 1 k 1 2 p 2 k 0 n x n k a 1 k n n k sin a x k p 2 sahrb n gt 0 displaystyle begin aligned int x n cos ax dx amp frac x n sin ax a frac n a int x n 1 sin ax dx amp sum k 0 2k 1 leq n 1 k frac x n 2k 1 a 2 2k frac n n 2k 1 cos ax sum k 0 2k leq n 1 k frac x n 2k a 1 2k frac n n 2k sin ax amp sum k 0 n 1 lfloor k 2 rfloor frac x n k a 1 k frac n n k cos left ax frac 1 k 1 2 frac pi 2 right amp sum k 0 n frac x n k a 1 k frac n n k sin left ax k frac pi 2 right qquad mbox sahrb n gt 0 mbox end aligned cos a x x d x ln a x k 1 1 k a x 2 k 2 k 2 k C displaystyle int frac cos ax x dx ln ax sum k 1 infty 1 k frac ax 2k 2k cdot 2k C cos a x x n d x cos a x n 1 x n 1 a n 1 sin a x x n 1 d x sahrb n 1 displaystyle int frac cos ax x n dx frac cos ax n 1 x n 1 frac a n 1 int frac sin ax x n 1 dx qquad mbox sahrb n neq 1 mbox d x cos a x 1 a ln tan a x 2 p 4 C displaystyle int frac dx cos ax frac 1 a ln left tan left frac ax 2 frac pi 4 right right C d x cos n a x sin a x a n 1 cos n 1 a x n 2 n 1 d x cos n 2 a x sahrb n gt 1 displaystyle int frac dx cos n ax frac sin ax a n 1 cos n 1 ax frac n 2 n 1 int frac dx cos n 2 ax qquad mbox sahrb n gt 1 mbox d x 1 cos a x 1 a tan a x 2 C displaystyle int frac dx 1 cos ax frac 1 a tan frac ax 2 C d x 1 cos a x 1 a cot a x 2 C displaystyle int frac dx 1 cos ax frac 1 a cot frac ax 2 C x d x 1 cos a x x a tan a x 2 2 a 2 ln cos a x 2 C displaystyle int frac x dx 1 cos ax frac x a tan frac ax 2 frac 2 a 2 ln left cos frac ax 2 right C x d x 1 cos a x x a cot a x 2 2 a 2 ln sin a x 2 C displaystyle int frac x dx 1 cos ax frac x a cot frac ax 2 frac 2 a 2 ln left sin frac ax 2 right C cos a x d x 1 cos a x x 1 a tan a x 2 C displaystyle int frac cos ax dx 1 cos ax x frac 1 a tan frac ax 2 C cos a x d x 1 cos a x x 1 a cot a x 2 C displaystyle int frac cos ax dx 1 cos ax x frac 1 a cot frac ax 2 C cos a 1 x cos a 2 x d x sin a 2 a 1 x 2 a 2 a 1 sin a 2 a 1 x 2 a 2 a 1 C sahrb a 1 a 2 displaystyle int cos a 1 x cos a 2 x dx frac sin a 2 a 1 x 2 a 2 a 1 frac sin a 2 a 1 x 2 a 2 a 1 C qquad mbox sahrb a 1 neq a 2 mbox priphthththiekiywkhxngechphaaaethnecnt aekikh tan a x d x 1 a ln cos a x C 1 a ln sec a x C displaystyle int tan ax dx frac 1 a ln cos ax C frac 1 a ln sec ax C tan 2 x d x tan x x C displaystyle int tan 2 x dx tan x x C tan n a x d x 1 a n 1 tan n 1 a x tan n 2 a x d x sahrb n 1 displaystyle int tan n ax dx frac 1 a n 1 tan n 1 ax int tan n 2 ax dx qquad mbox sahrb n neq 1 mbox d x q tan a x p 1 p 2 q 2 p x q a ln q sin a x p cos a x C sahrb p 2 q 2 0 displaystyle int frac dx q tan ax p frac 1 p 2 q 2 px frac q a ln q sin ax p cos ax C qquad mbox sahrb p 2 q 2 neq 0 mbox d x tan a x 1 x 2 1 2 a ln sin a x cos a x C displaystyle int frac dx tan ax 1 frac x 2 frac 1 2a ln sin ax cos ax C d x tan a x 1 x 2 1 2 a ln sin a x cos a x C displaystyle int frac dx tan ax 1 frac x 2 frac 1 2a ln sin ax cos ax C tan a x d x tan a x 1 x 2 1 2 a ln sin a x cos a x C displaystyle int frac tan ax dx tan ax 1 frac x 2 frac 1 2a ln sin ax cos ax C tan a x d x tan a x 1 x 2 1 2 a ln sin a x cos a x C displaystyle int frac tan ax dx tan ax 1 frac x 2 frac 1 2a ln sin ax cos ax C priphthththiekiywkhxngechphaaesaekhnt aekikh sec a x d x 1 a ln sec a x tan a x C displaystyle int sec ax dx frac 1 a ln left sec ax tan ax right C sec 2 x d x tan x C displaystyle int sec 2 x dx tan x C sec 3 x d x 1 2 sec x tan x 1 2 ln sec x tan x C displaystyle int sec 3 x dx frac 1 2 sec x tan x frac 1 2 ln sec x tan x C sec n a x d x sec n 2 a x tan a x a n 1 n 2 n 1 sec n 2 a x d x sahrb n 1 displaystyle int sec n ax dx frac sec n 2 ax tan ax a n 1 frac n 2 n 1 int sec n 2 ax dx qquad mbox sahrb n neq 1 mbox d x sec x 1 x tan x 2 C displaystyle int frac dx sec x 1 x tan frac x 2 C d x sec x 1 x cot x 2 C displaystyle int frac dx sec x 1 x cot frac x 2 C priphthththiekiywkhxngechphaaokhesaekhnt aekikh csc a x d x 1 a ln csc a x cot a x C displaystyle int csc ax dx frac 1 a ln left csc ax cot ax right C csc 2 x d x cot x C displaystyle int csc 2 x dx cot x C csc 3 x d x 1 2 csc x cot x 1 2 ln csc x cot x C displaystyle int csc 3 x dx frac 1 2 csc x cot x frac 1 2 ln csc x cot x C csc n a x d x csc n 2 a x cot a x a n 1 n 2 n 1 csc n 2 a x d x sahrb n 1 displaystyle int csc n ax dx frac csc n 2 ax cot ax a n 1 frac n 2 n 1 int csc n 2 ax dx qquad mbox sahrb n neq 1 mbox d x csc x 1 x 2 cot x 2 1 C displaystyle int frac dx csc x 1 x frac 2 cot frac x 2 1 C d x csc x 1 x 2 cot x 2 1 C displaystyle int frac dx csc x 1 x frac 2 cot frac x 2 1 C priphthththiekiywkhxngechphaaokhaethnecnt aekikh cot a x d x 1 a ln sin a x C displaystyle int cot ax dx frac 1 a ln sin ax C cot n a x d x 1 a n 1 cot n 1 a x cot n 2 a x d x sahrb n 1 displaystyle int cot n ax dx frac 1 a n 1 cot n 1 ax int cot n 2 ax dx qquad mbox sahrb n neq 1 mbox d x 1 cot a x tan a x d x tan a x 1 displaystyle int frac dx 1 cot ax int frac tan ax dx tan ax 1 d x 1 cot a x tan a x d x tan a x 1 displaystyle int frac dx 1 cot ax int frac tan ax dx tan ax 1 priphthththiekiywkhxngthngisnaelaokhisn aekikh d x cos a x sin a x 1 a 2 ln tan a x 2 p 8 C displaystyle int frac dx cos ax pm sin ax frac 1 a sqrt 2 ln left tan left frac ax 2 pm frac pi 8 right right C d x cos a x sin a x 2 1 2 a tan a x p 4 C displaystyle int frac dx cos ax pm sin ax 2 frac 1 2a tan left ax mp frac pi 4 right C d x cos x sin x n 1 n 1 sin x cos x cos x sin x n 1 2 n 2 d x cos x sin x n 2 displaystyle int frac dx cos x sin x n frac 1 n 1 left frac sin x cos x cos x sin x n 1 2 n 2 int frac dx cos x sin x n 2 right cos a x d x cos a x sin a x x 2 1 2 a ln sin a x cos a x C displaystyle int frac cos ax dx cos ax sin ax frac x 2 frac 1 2a ln left sin ax cos ax right C cos a x d x cos a x sin a x x 2 1 2 a ln sin a x cos a x C displaystyle int frac cos ax dx cos ax sin ax frac x 2 frac 1 2a ln left sin ax cos ax right C sin a x d x cos a x sin a x x 2 1 2 a ln sin a x cos a x C displaystyle int frac sin ax dx cos ax sin ax frac x 2 frac 1 2a ln left sin ax cos ax right C sin a x d x cos a x sin a x x 2 1 2 a ln sin a x cos a x C displaystyle int frac sin ax dx cos ax sin ax frac x 2 frac 1 2a ln left sin ax cos ax right C cos a x d x sin a x 1 cos a x 1 4 a tan 2 a x 2 1 2 a ln tan a x 2 C displaystyle int frac cos ax dx sin ax 1 cos ax frac 1 4a tan 2 frac ax 2 frac 1 2a ln left tan frac ax 2 right C cos a x d x sin a x 1 cos a x 1 4 a cot 2 a x 2 1 2 a ln tan a x 2 C displaystyle int frac cos ax dx sin ax 1 cos ax frac 1 4a cot 2 frac ax 2 frac 1 2a ln left tan frac ax 2 right C sin a x d x cos a x 1 sin a x 1 4 a cot 2 a x 2 p 4 1 2 a ln tan a x 2 p 4 C displaystyle int frac sin ax dx cos ax 1 sin ax frac 1 4a cot 2 left frac ax 2 frac pi 4 right frac 1 2a ln left tan left frac ax 2 frac pi 4 right right C sin a x d x cos a x 1 sin a x 1 4 a tan 2 a x 2 p 4 1 2 a ln tan a x 2 p 4 C displaystyle int frac sin ax dx cos ax 1 sin ax frac 1 4a tan 2 left frac ax 2 frac pi 4 right frac 1 2a ln left tan left frac ax 2 frac pi 4 right right C sin a x cos a x d x 1 2 a sin 2 a x C displaystyle int sin ax cos ax dx frac 1 2a sin 2 ax C sin a 1 x cos a 2 x d x cos a 1 a 2 x 2 a 1 a 2 cos a 1 a 2 x 2 a 1 a 2 C sahrb a 1 a 2 displaystyle int sin a 1 x cos a 2 x dx frac cos a 1 a 2 x 2 a 1 a 2 frac cos a 1 a 2 x 2 a 1 a 2 C qquad mbox sahrb a 1 neq a 2 mbox sin n a x cos a x d x 1 a n 1 sin n 1 a x C sahrb n 1 displaystyle int sin n ax cos ax dx frac 1 a n 1 sin n 1 ax C qquad mbox sahrb n neq 1 mbox sin a x cos n a x d x 1 a n 1 cos n 1 a x C sahrb n 1 displaystyle int sin ax cos n ax dx frac 1 a n 1 cos n 1 ax C qquad mbox sahrb n neq 1 mbox sin n a x cos m a x d x sin n 1 a x cos m 1 a x a n m n 1 n m sin n 2 a x cos m a x d x sahrb m n gt 0 sin n 1 a x cos m 1 a x a n m m 1 n m sin n a x cos m 2 a x d x sahrb m n gt 0 displaystyle begin aligned int sin n ax cos m ax dx amp frac sin n 1 ax cos m 1 ax a n m frac n 1 n m int sin n 2 ax cos m ax dx qquad mbox sahrb m n gt 0 mbox amp frac sin n 1 ax cos m 1 ax a n m frac m 1 n m int sin n ax cos m 2 ax dx qquad mbox sahrb m n gt 0 mbox end aligned d x sin a x cos a x 1 a ln tan a x C displaystyle int frac dx sin ax cos ax frac 1 a ln left tan ax right C d x sin a x cos n a x 1 a n 1 cos n 1 a x d x sin a x cos n 2 a x sahrb n 1 displaystyle int frac dx sin ax cos n ax frac 1 a n 1 cos n 1 ax int frac dx sin ax cos n 2 ax qquad mbox sahrb n neq 1 mbox d x sin n a x cos a x 1 a n 1 sin n 1 a x d x sin n 2 a x cos a x sahrb n 1 displaystyle int frac dx sin n ax cos ax frac 1 a n 1 sin n 1 ax int frac dx sin n 2 ax cos ax qquad mbox sahrb n neq 1 mbox sin a x d x cos n a x 1 a n 1 cos n 1 a x C sahrb n 1 displaystyle int frac sin ax dx cos n ax frac 1 a n 1 cos n 1 ax C qquad mbox sahrb n neq 1 mbox sin 2 a x d x cos a x 1 a sin a x 1 a ln tan p 4 a x 2 C displaystyle int frac sin 2 ax dx cos ax frac 1 a sin ax frac 1 a ln left tan left frac pi 4 frac ax 2 right right C sin 2 a x d x cos n a x sin a x a n 1 cos n 1 a x 1 n 1 d x cos n 2 a x sahrb n 1 displaystyle int frac sin 2 ax dx cos n ax frac sin ax a n 1 cos n 1 ax frac 1 n 1 int frac dx cos n 2 ax qquad mbox sahrb n neq 1 mbox sin n a x d x cos a x sin n 1 a x a n 1 sin n 2 a x d x cos a x sahrb n 1 displaystyle int frac sin n ax dx cos ax frac sin n 1 ax a n 1 int frac sin n 2 ax dx cos ax qquad mbox sahrb n neq 1 mbox sin n a x d x cos m a x sin n 1 a x a m 1 cos m 1 a x n m 2 m 1 sin n a x d x cos m 2 a x sahrb m 1 sin n 1 a x a m 1 cos m 1 a x n 1 m 1 sin n 2 a x d x cos m 2 a x sahrb m 1 sin n 1 a x a n m cos m 1 a x n 1 n m sin n 2 a x d x cos m a x sahrb m n displaystyle int frac sin n ax dx cos m ax begin cases frac sin n 1 ax a m 1 cos m 1 ax frac n m 2 m 1 int frac sin n ax dx cos m 2 ax amp mbox sahrb m neq 1 mbox frac sin n 1 ax a m 1 cos m 1 ax frac n 1 m 1 int frac sin n 2 ax dx cos m 2 ax amp mbox sahrb m neq 1 mbox frac sin n 1 ax a n m cos m 1 ax frac n 1 n m int frac sin n 2 ax dx cos m ax amp mbox sahrb m neq n mbox end cases cos a x d x sin n a x 1 a n 1 sin n 1 a x C sahrb n 1 displaystyle int frac cos ax dx sin n ax frac 1 a n 1 sin n 1 ax C qquad mbox sahrb n neq 1 mbox cos 2 a x d x sin a x 1 a cos a x ln tan a x 2 C displaystyle int frac cos 2 ax dx sin ax frac 1 a left cos ax ln left tan frac ax 2 right right C cos 2 a x d x sin n a x 1 n 1 cos a x a sin n 1 a x d x sin n 2 a x sahrb n 1 displaystyle int frac cos 2 ax dx sin n ax frac 1 n 1 left frac cos ax a sin n 1 ax int frac dx sin n 2 ax right qquad mbox sahrb n neq 1 mbox cos n a x d x sin m a x cos n 1 a x a m 1 sin m 1 a x n m 2 m 1 cos n a x d x sin m 2 a x sahrb m 1 cos n 1 a x a m 1 sin m 1 a x n 1 m 1 cos n 2 a x d x sin m 2 a x sahrb m 1 cos n 1 a x a n m sin m 1 a x n 1 n m cos n 2 a x d x sin m a x sahrb m n displaystyle int frac cos n ax dx sin m ax begin cases frac cos n 1 ax a m 1 sin m 1 ax frac n m 2 m 1 int frac cos n ax dx sin m 2 ax amp mbox sahrb m neq 1 mbox frac cos n 1 ax a m 1 sin m 1 ax frac n 1 m 1 int frac cos n 2 ax dx sin m 2 ax amp mbox sahrb m neq 1 mbox frac cos n 1 ax a n m sin m 1 ax frac n 1 n m int frac cos n 2 ax dx sin m ax amp mbox sahrb m neq n mbox end cases priphthththiekiywkhxngthngisnaelaaethnecnt aekikh sin a x tan a x d x 1 a ln sec a x tan a x sin a x C displaystyle int sin ax tan ax dx frac 1 a ln sec ax tan ax sin ax C tan n a x d x sin 2 a x 1 a n 1 tan n 1 a x C sahrb n 1 displaystyle int frac tan n ax dx sin 2 ax frac 1 a n 1 tan n 1 ax C qquad mbox sahrb n neq 1 mbox priphthththiekiywkhxngthngokhisnaelaaethnecnt aekikh tan n a x d x cos 2 a x 1 a n 1 tan n 1 a x C sahrb n 1 displaystyle int frac tan n ax dx cos 2 ax frac 1 a n 1 tan n 1 ax C qquad mbox sahrb n neq 1 mbox priphthththiekiywkhxngthngisnaelaokhaethnecnt aekikh cot n a x d x sin 2 a x 1 a n 1 cot n 1 a x C sahrb n 1 displaystyle int frac cot n ax dx sin 2 ax frac 1 a n 1 cot n 1 ax C qquad mbox sahrb n neq 1 mbox priphthththiekiywkhxngthngokhisnaelaokhaethnecnt aekikh cot n a x d x cos 2 a x 1 a 1 n tan 1 n a x C sahrb n 1 displaystyle int frac cot n ax dx cos 2 ax frac 1 a 1 n tan 1 n ax C qquad mbox sahrb n neq 1 mbox priphthththiekiywkhxngthngesaekhntaelaaethnecnt aekikh sec x tan x d x sec x C displaystyle int sec x tan x dx sec x C priphthththiekiywkhxngthngokhesaekhntaelaokhaethnecnt aekikh csc x cot x d x csc x C displaystyle int csc x cot x dx csc x C ekhathungcak https th wikipedia org w index php title raykarpriphnthkhxngfngkchntrioknmiti amp oldid 7539021, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,