Question

Evaluate the following integrals:
i) ∫ [1/(1+x²)tan^-1x]dx

Answer 1

$\int{\frac{atan(x)dx}{1+x^2}}=(u=atan(x),\;du=\frac{dx}{1+x^2})=\int{udu}=\frac{u^2}{2}+C=\frac{(atan(x))^2}{2}+C$