Question

For the integral \[\int_{0}^{1}\frac{\tan^{-1}x}{1+x^2}\,dx\], which substitution is suitable?

Options

• \[t=1+x^2\]

• \[t=\tan^{-1}x\]

• \[t=\frac{1}{1+x^2}\]

• \[t=\tan x\]

Answer 1

The integrand contains the inner function \[\tan^{-1}x\]. Its derivative is \[\frac{1}{1+x^2}\], which is also present in the integrand.