Question

evaluate the indefinite integral.
sec(x)^21tan(x)dx

Answer 1

alright , we have :\[\int\limits \sec^{21}(x)\tan(x) dx\]


you can write it down as :

\[\int\limits \sec^{20}(x) \tan(x)\sec(x) dx\]
now let :

u = sec(x)
du = tan(x)sec(x)

so now you'll get:

\[\int\limits u^{20} du = \frac{u^{21}}{21} + c\]
\[= \frac{\sec^{21}(x)}{21} + c\]

correct me if I'm wrong ^_^