∫(0 1)x(arctanx)^2dx

问题描述:

∫(0 1)x(arctanx)^2dx

∫[0→1] xarctan²x dx=(1/2)∫[0→1] arctan²x d(x²)=(1/2)x²arctan²x - ∫[0→1] x²arctanx/(1+x²) dx=(1/2)x²arctan²x - ∫[0→1] (x²+1-1)arctanx/(1+x²...