Question

integration of 1/(1+x^2)

Answer 1

Step-by-step explanation:

We have,

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

Let $x= tan(θ)$

$\implies dx= \sec^{2}(\theta) d\theta$

$= \int \frac{ \sec^{2} ( \theta) d \theta}{{ \sec}^{2}( \theta) }$

$= \int d \theta$

$= \theta + c$

$= \tan^{ - 1} (x) + c$