计算d/dx∫(x,0)(x/(1+t^2)dt)

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计算d/dx∫(x,0)(x/(1+t^2)dt)计算d/dx∫(x,0)(x/(1+t^2)dt)计算d/dx∫(x,0)(x/(1+t^2)dt)∫(x,0)(x/(1+t^2)dt)lett=t

计算d/dx∫(x,0)(x/(1+t^2)dt)
计算d/dx∫(x,0)(x/(1+t^2)dt)

计算d/dx∫(x,0)(x/(1+t^2)dt)
∫(x,0)(x/(1+t^2)dt)
let
t = tana
dt = (seca)^2 da
t = 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)