Question

Evaluate \[\int \frac{dx}{1+x^2}\]

Options

• \[\log|x|+\mathrm{C}\]

• \[\tan^{-1}x+\mathrm{C}\]

• \[\sin^{-1}x+\mathrm{C}\]

• \[\frac{1}{1+x^2}+\mathrm{C}\]

Answer 1

The derivative of \(\tan^{-1}x\) is \(\frac{1}{1+x^2}\). Hence, \(\int \frac{dx}{1+x^2}=\tan^{-1}x+\mathrm{C}\).