Question

求解答，微积分∫arcsinxdx要详细步骤

Answer 1

令U=arcsinx U'=1/√(1-x^2)dx

V'=dx V=x

∫arcsinxdx=UV-∫VU'

=x*arcsinx-∫x/√(1-x^2)dx

=x*arcsinx-0.5∫1/√(1-x^2)dx^2

=x*arcsinx+0.5∫1/√(1-x^2)d(1-x^2)

=x*arcsinx+√(1-x^2)