Question

integration of e^log(1+1/x²)​

Answer 1

Answer:

Explanation:

$Let I=∫log(1+x2)dx =∫log(1+x2)∗(1)dx by using integration by parts∴I=log(1+x2)∫1dx−∫ddxlog(1+x2)∫1dxdx =xlog(1+x2)−∫2x21+x2dx =xlog(1+x2)−2∫x21+x2dx Let I1=∫x21+x2 =∫x2+1–11+x2dx =∫x2+1x2+1dx−∫11+x2dx =x−tan−1x−C ∴ Now I=xlog(1+x2)−2I1 ⟹I=xlog(1+x2)−2x+2tan−1x+C$

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Answer 2

Answer:

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