Question

$\int \frac{d}{dx}\left({\tan }^{-1}x\right)dx=$_______$+c$

Answer 1

We have,

$\int \frac{d}{dx}\left({\tan }^{-1}x\right)dx$

On first differentiating and we get,

$\int \frac{1}{1+x^2}dx$

On integrating and we get,

$\int \frac{1}{1+x^2}dx={\tan }^{-1}x+c$

Hence, this is the answer.