∫上限正无穷下限0 arctanx/(1+x^2)^(3/2)dx
问题描述：
∫上限正无穷下限0 arctanx/(1+x^2)^(3/2)dx
答
π/2-1
答
∫(0->+∞) arctanx / (1+x^2)^(3/2)dxletx= tanadx= (seca)^2 dax=0,a=0x=+∞,a=π/2∫(0->+∞) arctanx / (1+x^2)^(3/2)dx=∫(0->π/2) [a / (seca)^3 ] (seca)^2 da=∫(0->π/2) acosa da=∫(0->π/2) adsina=[as...