Question

log (1+x^2) 1x integrate it by parts ​

Answer 1

Answer:

LetI=∫log(1+x2)dx

=∫log(1+x2)∗(1)dx

by using integration by parts

∴I=log(1+x2)∫1dx−∫ddxlog(1+x2)∫1dxdx

=xlog(1+x2)−∫2x21+x2dx

=xlog(1+x2)−2∫x21+x2dx

Let I1=∫x21+x2

=∫x2+1–11+x2dx

=∫x2+1x2+1dx−∫11+x2dx

=x−tan−1x−C

∴ Now I=xlog(1+x2)−2I1

⟹I=xlog(1+x2)−2x+2tan−1x+C

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