តារាងអាំងតេក្រាលនៃអនុគមន៍ច្រាស់ត្រីកោណមាត្រ

ខាងក្រោមនេះជាតារាងអាំងតេក្រាល (ព្រីមីទីវ) នៃអនុគមន៍ច្រាស់ត្រីកោណមាត្រ។ សំរាប់តារាងពេញលេញ សូមមើលតារាងអាំងតេក្រាល។ ចំនាំ៖ អក្សរកាត់របស់អនុគមន៍ច្រាស់ត្រីកោណមាត្រអាចសរសេរ​តាមរបៀបបីយ៉ាង។ ឧទាហរណ៍ អនុគមន៍អាកស៊ីនុសអាចសរសេរជា sin⁻¹, asin, ឬ arcsin។ នៅក្នុងអត្ថបទនេះ យើងជ្រើសរើសយកការសរសេរ arcsin ដែលគេនិយមសរសេរ។

${\displaystyle \int \arcsin x\,dx=x\arcsin x+{\sqrt {1-x^{2}$

${\displaystyle \int \arcsin {\frac {x}{c}\ dx=x\arcsin {\frac {x}{c}+{\sqrt {c^{2}-x^{2}$

${\displaystyle \int x\arcsin {\frac {x}{c}\ dx=\left({\frac {x^{2}{2}-{\frac {c^{2}{4}\right)\arcsin {\frac {x}{c}+{\frac {x}{4}{\sqrt {c^{2}-x^{2}$

${\displaystyle \int x^{2}\arcsin {\frac {x}{c}\ dx={\frac {x^{3}{3}\arcsin {\frac {x}{c}+{\frac {x^{2}+2c^{2}{9}{\sqrt {c^{2}-x^{2}$

${\displaystyle \int x^{n}\arcsin x\ dx={\frac {1}{n+1}\left(x^{n+1}\arcsin x+{\frac {x^{n}{\sqrt {1-x^{2}-nx^{n-1}\arcsin x}{n-1}+n\int x^{n-2}\arcsin x\ dx\right)}$

${\displaystyle \int \arccos x\,dx=x\arccos x-{\sqrt {1-x^{2}$

${\displaystyle \int \arccos {\frac {x}{c}\ dx=x\arccos {\frac {x}{c}-{\sqrt {c^{2}-x^{2}$

${\displaystyle \int x\arccos {\frac {x}{c}\ dx=\left({\frac {x^{2}{2}-{\frac {c^{2}{4}\right)\arccos {\frac {x}{c}-{\frac {x}{4}{\sqrt {c^{2}-x^{2}$

${\displaystyle \int x^{2}\arccos {\frac {x}{c}\ dx={\frac {x^{3}{3}\arccos {\frac {x}{c}-{\frac {x^{2}+2c^{2}{9}{\sqrt {c^{2}-x^{2}$

${\displaystyle \int \arctan x\,dx=x\arctan x-{\frac {1}{2}\ln |1+x^{2}|}$

${\displaystyle \int \arctan {\big (}{\frac {x}{c}{\big )}dx=x\arctan {\big (}{\frac {x}{c}{\big )}-{\frac {c}{2}\ln(1+{\frac {x^{2}{c^{2})}$

${\displaystyle \int x\arctan {\big (}{\frac {x}{c}{\big )}dx={\frac {(c^{2}+x^{2})\arctan {\big (}{\frac {x}{c}{\big )}-cx}{2}$

${\displaystyle \int x^{2}\arctan {\big (}{\frac {x}{c}{\big )}dx={\frac {x^{3}{3}\arctan {\big (}{\frac {x}{c}{\big )}-{\frac {cx^{2}{6}+{\frac {c^{3}{6}\ln |{c^{2}+x^{2}|}$

${\displaystyle \int x^{n}\arctan {\big (}{\frac {x}{c}{\big )}dx={\frac {x^{n+1}{n+1}\arctan {\big (}{\frac {x}{c}{\big )}-{\frac {c}{n+1}\int {\frac {x^{n+1}{c^{2}+x^{2}\ dx,\quad n\neq -1}$

${\displaystyle \int \operatorname {arccsc} x\,dx=x\operatorname {arccsc} x+\ln \left|x+x{\sqrt {x^{2}-1} \over x^{2}\right|}$

${\displaystyle \int \operatorname {arccsc} {\frac {x}{c}\ dx=x\operatorname {arccsc} {\frac {x}{c}+{c}\ln {({\frac {x}{c}({\sqrt {1-{\frac {c^{2}{x^{2}+1))}$

${\displaystyle \int x\operatorname {arccsc} {\frac {x}{c}\ dx={\frac {x^{2}{2}\operatorname {arccsc} {\frac {x}{c}+{\frac {cx}{2}{\sqrt {1-{\frac {c^{2}{x^{2}$

${\displaystyle \int \operatorname {arcsec} x\,dx=x\operatorname {arcsec} x-\ln \left|x+x{\sqrt {x^{2}-1} \over x^{2}\right|}$

${\displaystyle \int \operatorname {arcsec} {\frac {x}{c}\ dx=x\operatorname {arcsec} {\frac {x}{c}+{\frac {x}{c|x|}\ln \left|x\pm {\sqrt {x^{2}-1}\right|}$

${\displaystyle \int x\operatorname {arcsec} x\ dx={\frac {1}{2}\left(x^{2}\operatorname {arcsec} x-{\sqrt {x^{2}-1}\right)}$

${\displaystyle \int x^{n}\operatorname {arcsec} x\ dx={\frac {1}{n+1}\left(x^{n+1}\operatorname {arcsec} x-{\frac {1}{n}\left[x^{n-1}{\sqrt {x^{2}-1}+(1-n)\left(x^{n-1}\operatorname {arcsec} x+(1-n)\int x^{n-2}\operatorname {arcsec} x\ dx\right)\right]\right)}$

${\displaystyle \int \operatorname {arccot} x\,dx=x\operatorname {arccot} x+{\frac {1}{2}\ln |1+x^{2}|}$

${\displaystyle \int \operatorname {arccot} {\frac {x}{c}\ dx=x\operatorname {arccot} {\frac {x}{c}+{\frac {c}{2}\ln(c^{2}+x^{2})}$

${\displaystyle \int x\operatorname {arccot} {\frac {x}{c}\ dx={\frac {c^{2}+x^{2}{2}\operatorname {arccot} {\frac {x}{c}+{\frac {cx}{2}$

${\displaystyle \int x^{2}\operatorname {arccot} {\frac {x}{c}\ dx={\frac {x^{3}{3}\operatorname {arccot} {\frac {x}{c}+{\frac {cx^{2}{6}-{\frac {c^{3}{6}\ln(c^{2}+x^{2})}$

${\displaystyle \int x^{n}\operatorname {arccot} {\frac {x}{c}\ dx={\frac {x^{n+1}{n+1}\operatorname {arccot} {\frac {x}{c}+{\frac {c}{n+1}\int {\frac {x^{n+1}{c^{2}+x^{2}\ dx,\quad n\neq 1}$