Question

Integration:

Answer 1

\[\LARGE \int~x^5\sqrt{x^2+4}~dx\]

Answer 2

sub x = 2tanu
dx = 2sec^2u du

Answer 3

\[4 \int\limits 32\tan^5u \sec^3u du ~~ = 128 \int\limits \tan^5u \sec^3u du\]

Answer 4

Use the trig identitiy tan^2x = sec^2x -1

\[128 \int\limits tanu \sec^3u (\sec^2u - 1)^2 du\]

sub t = sec u
dt = tanusecu du

\[= 128 \int\limits t^2(t^2-1)^2 dt\]

Expand it

\[= 128 \int\limits (t^6-2t^4+t^2) dt\]

Pretty straight forward from there, and ofc you'd leave >_>

Answer 5

I'm right here, I never left bro.

And that sub the only way? Or is it just the "best" sub?

Answer 6

There's always more than one way, but I wanted to do it that way, it's good practice. And omg you changed your picture, I usually expect a baby luigi or something, quit changing your pic.

Answer 7

You could try parts, not sure how far you'll get but it's worth a shot.

Answer 8

Thanks bud :)