三角関数の原始関数の一覧
∫ d x sin  a x = 1 a ln  | tan  a x 2 | + C {\displaystyle \int {\frac {\mathrm {d} x}{\sin ax}}={\frac {1}{a}}\ln \left|\tan {\frac {ax}{2}}\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 ( n > 1 ) {\displaystyle \int {\frac {\mathrm {d} x}{\sin ^{n}ax}}={\frac {\cos ax}{a(1-n)\sin ^{n-1}ax}}+{\frac {n-2}{n-1}}\int {\frac {\mathrm {d} x}{\sin ^{n-2}ax}}\qquad {\mbox{(}}n>1{\mbox{)}}\,\!}
∫ x sin  a x d x = sin  a x a 2 − x cos  a x a + C {\displaystyle \int x\sin ax\;\mathrm {d} x={\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 !