Answer to Question #162041 in Calculus for Phyroe

Question

Evaluate the integral of (tan^-1 x)/(1+x² )dx from 0 to1

Answer 1

Evaluate the integral of (tan^-1 x)/(1+x² )dx from 0 to1

Let $u=tan^{-1}x$

Then ${du \over dx}={1 \over 1+x^2}$

$dx=(1+x²)du$

$\int_0 {u \over 1+x²}.(1+x²)du$

=${u² \over 2}= {(tan^{-1}x)^2 \over 2}$ From 0 to 1

${(tan^{-1}1)² \over 2}-{(tan^{-1}0)² \over 2}$

${(tan^{-1}1)² \over 2}$