Question

用分部积分法计算不定积分∫arcsinxdx还请大大们给个过程,谢谢!

Answer 1

原式=xarcsinx-∫xdarcsinx

=xarcsinx-∫xdx/√(1-x²)

=xarcsinx-1/2∫dx²/√(1-x²)

=xarcsinx+1/2∫(1-x²)^(-1/2)d(1-x²)

=xarcsinx+1/2*(1-x²)^(-1/2+1)/(-1/2+1)+C

=xarcsinx+(1-x²)^(1/2)+C

=xarcsinx+√(1-x²)+C