Question

integration of csc^2 x*sec^2 x dx

Answer 1

please type by latex

Answer 2

\[\int\limits_{}^{} \csc ^{2}xsec ^{2}x dx\]

Answer 3

\[\int\limits {\frac{dx}{\cos^2 x \sin^2 x}}=\int\limits {\frac{dx}{\cos^2 x}} + \int\limits {\frac{dx}{\sin^2 x}}\]
Try to have a next step :)

Answer 4

you have \[1=\sin^2 x +\cos^2 x\] in numerator, so we can divide into a sum above.

Answer 5

Notice that
\[
\csc ^2(x) \sec ^2(x)=4 \csc
^2(2 x) \\
\]
This comes from the fact
\[
\sin(2 x) = 2 \sin(x) \cos(x)
\]
Notice that the derivative of cot(2x) is

\[
-2 \csc ^2(2 x)
\]
You can now deduce your integral.