Question

integrate tan^7 (x/2) sec^2 (x/2) dx. pleaseee.

Answer 1

d tan(x/2) =(1/2)sec^2 (x/2)
integrate tan^7 (x/2) sec^2 (x/2) dx
=integrate tan^7 (x/2) d 2tan(x/2)
=2 integrate tan^7 (x/2) d tan(x/2)
=2 (1/8)tan^8 (x/2) +C

Answer 2

substitute\[u = \tan \left( \frac{x}{2} \right)\]\[du = \frac{1}{2}\sec^{2}\left( \frac{x}{2} \right)dx\]

Answer 3

\(u=\tan(\frac{x}{2}), du=\frac{1}{2}\sec^2(\frac{x}{2})dx\) get
\[\frac{1}{2}\int u^7du\] etc

Answer 4

oops should be \(2\int u^7du\) since it is \(2du=\sec^2(\frac{x}{2})dx\)