逆三角関数の原始関数の一覧
∫ arcsin  x d x = x arcsin  x + 1 − x 2 + C {\displaystyle \int \arcsin x\,dx=x\arcsin x+{\sqrt {1-x^{2}}}+C}
∫ arcsin  a x d x = x arcsin  a x + 1 − a 2 x 2 a + C {\displaystyle \int \arcsin ax\,dx=x\arcsin ax+{\frac {\sqrt {1-a^{2}x^{2}}}{a}}+C}
∫ x arcsin  a x d x = x 2 arcsin  a x 2 − arcsin  a x 4 a 2 + x 1 − a 2 x 2 4 a + C {\displaystyle \int x\arcsin ax\,dx={\frac {x^{2}\arcsin ax}{2}}-{\frac {\arcsin ax}{4a^{2}}}+{\frac {x{\sqrt {1-a^{2}x^{2}}}}{4\,a}}+C}
∫ x 2 arcsin  a x d x = x 3 arcsin  a x 3 + ( a 2 x 2 + 2 ) 1 − a 2 x 2 9 a 3 + C {\displaystyle \int x^{2}\arcsin ax\,dx={\frac {x^{3}\arcsin ax}{3}}+{\frac {\left(a^{2}x^{2}+2\right){\sqrt {1-a^{2}x^{2}}}}{9\,a^{3}}}+C}