How do you find the integral of $(1+x) / (1+x^2)$ ?

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Answer 1 · 2015-09-22T17:25:40

$arctanx+1/2ln(1+x^2)+C$

$int (1+x)/(1+x^2)dx=int 1/(1+x^2)dx + int x/(1+x^2)dx = I$

Let:
$t = 1+x^2$
$dt = 2xdx => xdx=dt/2$

$I = arctanx+1/2int 1/t dt$

$= color(blue)(arctanx+1/2ln(1+x^2)+C)$

How do you find the integral of (1+x) / (1+x^2)(1+x) / (1+x^2)?