Question

Solve Integral

Answer 1

\[\int\limits_{}^{} \sec^2x cosec^2x dx\]

Answer 2

\[2\csc(2x) \implies \sec x \csc x\]
right? so...
\[\sec^2 x \csc ^2 x \implies 4\csc^2 (2x)\]
so the integral becomes \[\int 4\csc^2 (2x) dx\]
does that help?

Answer 3

rewrite the integrand\[\sec^2 x \csc ^2 x = \frac{1}{\cos^2 x \sin ^2 x}\]\[= \frac{1}{(\sin x \cos x)^2 }\]\[= \frac{1}{\left(\frac{1}{2}\sin 2x\right)^2}\]\[= 4 \csc^2 (2x)\]

Answer 4

and another one maybe this help :\[\sec^2 x \ \text{cosec}^2x=(1+\tan^2 x)(1+\cot^2 x)=1+\tan^2 x+(1+\tan^2 x)\cot^2 x\]

Answer 5

Oh ! Nice one there everybody.. I got into integration by parts LOL !!

Answer 6

Thanx all