计算d/dx∫(x,0)(x/(1+t^2)dt)
问题描述：
计算d/dx∫(x,0)(x/(1+t^2)dt)
答
∫(x,0)(x/(1+t^2)dt)let t = tanadt = (seca)^2 dat = x,a =arctan(x)t =0,a = 0∫(x,0)(x/(1+t^2)dt)=∫(arctan(x),0)xda= x [a](arctan(x),0)= x( arctanx )d/dx(∫(x,0)(x/(1+t^2)dt)) = arctanx + x/(1+x^2)...