‹ Back to the paper
Solve the following.
Evaluate: ∫ (sec² x)/(cosec² x) dx
Evaluate: $\int \frac{\sec^2 x}{\operatorname{cosec}^2 x}\,dx$
Answer
Answer
Integral: $\int \left(tan(x)^2\right) dx$
$\frac{\sec^2 x}{\operatorname{cosec}^2 x} = \frac{\sin^2 x}{\cos^2 x} = \tan^2 x = \sec^2 x - 1$
$\int (\sec^2 x - 1)\,dx = \tan x - x + C$
Hence the integral is $\tan x - x + C$.
Final answer: $\tan x - x + C$