Question

Integral:

Answer 1

\[\int\limits_{}^{}\frac{ 1 }{ \sin^2(2x) }dx\]

Answer 2

What is the integral of csc ^2 x ?

Answer 3

@shailkumar it's not a usually one you don't need to know all the tables from universe

Answer 4

if you are writing 1 as sin^2(x)+cos^2(x)=>
\[x+\int\limits_{}^{}cotan^2(2x)\]

Answer 5

Ok. But integral of csc^2 x, you should know. It is -cot x. Your integral is \[\int\limits \csc^2 2x dx\]
= -cot 2x /2

Answer 6

Of course an additive constant.

Answer 7

it's not in my tables but I've kind found a way to solve it watch it
\[\sin(2x)=2sinxcosx=>\int\limits_{}^{}(2\sin(x)\cos(x))^{-2} dx\]

Answer 8

now if we substitute sin(x)=t=>cosxdx=dt

Answer 9

so far good, then ?

Answer 10

You will be stuck to handle the swinging -2.

Answer 11

Ok. what is the derivative of cot x ?

Answer 12

Integ (1/sin^2 (2x) dx
= -1/2 cot (2x) +c

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