Question

Integrate 1/(sin²x cos²x) with respect to x.

sin²x + cos²x = 1

Answer 1

\(\int \frac 1{\sin^2x\cos^2x}dx\)

\(= \int \frac{sin^2x + cos^2x}{sin^2x\cos^2x} dx\)    (Using sin²x + cos²x = 1)

\(= \int \frac{\sin^2x}{\sin^2x \cos^2x}dx + \int \frac {\cos^2 x}{\sin^2x\cos^2x}dx\)

\(= \int \frac 1{\cos^2x} dx + \int \frac 1{\sin^2x}dx\)

\(= \int \sec^2x dx + \int cosec^2x\, dx\)

\(= \tan x - \cot x + C\)

Answer 2

1/(sin²x cos²x )