∫x√(1-x2)arcsinxdx

∫x√(1-x²)arcsinxdx
【正确答案】：∫x√(1-x²)arcsinxdx =-1/2∫(1-x²)^1/2•arcsinxd(1-x²) =-1/3arcsinxd(1-x²)^3/2 =-1/3√(1-x²)³•arcsinx+1/3∫(1-x²)^3/2darcsinx =-1/3√(1-x²)³•arcsinx+1/3∫(1-x²)dx =-1/3√(1-x²)³•arcsinx+1/3x-1/9x³+C