Question

Find $\int \frac{(x^2+{\sin }^{2}x){\sec }^{2}x}{1+x^2}dx$

Answer 1

$\int \frac{(x^2+{\sin }^{2}x){\sec }^{2}x}{1+x^2}\cdot dx$

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

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

$\int \frac{{\sec }^{2}x(1+x^2)-1}{1+x^2}\cdot dx$

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

$\tan x-{\tan }^{-1}x+c$.