Question

find the indefinite integral

Answer 1

\[\int\limits \sec^5(2x) \tan(2x)dx\]

Answer 2

u= sec(2 x)
du= 2 sec(2 x) tan(2 x) dx
\[
\int u^4 \frac {du}2 = \frac {u^5}{10} + C=\frac {\sec^5(2x)}{10}+C
\]

Answer 3

eliassaab's answer is perfect, if you happen to have trouble with trigonometric identities you can also use the standard definitions of sec(x) and tan(x) to obtain the following integral:

\[ \int \frac{sin(2x)}{cos^6{(2x)}} \]
then I recommend an u-Substitution for cos(2x)