Question

Integrate:

∫dx / (sin²x⋅cos²x) equals?

Answer 1

Consider the given integration,

⇒∫dx / sin²x.cos²x

⇒∫4dx/ 4sin²x.cos²x

⇒∫4dx/ (2sinx cosx )² = ∫4dx/ (sin 2x )²

⇒4∫cosec²2x dx

⇒4(−cot2x)/2+C

⇒−2cot2x+C

Hence, this is the answer.