企源知识库

∫[xarcsinx/(1-x²)^3/2]dx
【正确答案】：∫[xarcsinx/(1-x²)^3/2]dx =-1/2∫arcsinx(1-x²)^-(3/2)d(1-x²) =-1/2∫arcsinxd [-2(1-x²)^-(1/2) =∫arcsinxd[1/√(1-x²)] =arcsinxd/√(1-x²)-∫(1/√(1-x²)darcsinx =arcsinx/1/√(1-x²)-∫1/(1-x²)dx =arcsinx/√(1-x²)-(1/2)ln|(1+x)/(1-x)|+C．