How do you integrate $int4sec4xtan4xsec^4 4x$ using substitution?

Question

2466 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-16T23:16:08

Well, let's rewrite this, and you may see something.

Let $u = 4x$ , and you have $du = 4dx$ .

$color(blue)(int 4sec4xtan4xsec^4 (4x)dx)$

$= int secutanusec^4(u)du$

So now... let $v = secu$ , and you get $dv = secutanudu$ :

$=> int (secu)^4secutanudu$

$= int v^4dv$

$= v^5/5$

Back-substitute to get:

$= sec^5(u)/5$

$= color(blue)(sec^5(4x)/5 + C)$

How do you integrate int4sec4x*tan4x*sec^4 4xint4sec4x*tan4x*sec^4 4x using substitution?