Question

Evaluate:
$\int ({\cot }^{2}2x+{\tan }^{2}3x)dx$

Answer 1

Given : $\int ({\cot }^{2}2x+{\tan }^{2}3x)dx$

$\int ({\cot }^{2}2x+{\tan }^{2}3x)dx=\int {(\text{cosec}}^{2}2x+{\sec }^{2}3x-2)dx=-\frac{1}{2}\cot x+\frac{1}{3}\tan x-2x+C$

Hence the correct answer is $-\frac{1}{2}\cot x+\frac{1}{3}\tan x-2x+C$