Question

求积分∫arcsinXdx

请高手帮帮忙，请问∫arcsinXdx等于多少？请写出详细解答步骤，谢谢~~~

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)