Question

Find the indefinite integral:

Answer 1

\[\frac{ (x+5)dx }{ (\sqrt{x}-3)^{\frac{ 3 }{ 2 }}}\]

Answer 2

Wow this thing requires something like a double substitution D:

Answer 3

I was thinking of a doing a trig sub

what about you @Jhannybean ?

Answer 4

double u-sub

Answer 5

oh just 2 algebraic subs
that would be a lot more cute

Answer 6

Or uh what do you call it, a u-sub and then like a z sub or something, something that replaces the u.

Answer 7

\(\boxed{`cute`}\) haha.

Answer 8

I'm just going to paste the wolfram partial solution here.

Answer 9

and you want to look at the trig sub
i think this should work
\[\sqrt[4]{x}=\sqrt{3} \sec(\theta) \\ \sqrt{x}=3 \sec^2(\theta) \\ x=9 \sec^4( \theta) \\ dx=36\sec^3(\theta) \sec(\theta) \tan(\theta) d \theta \]

Answer 10

Ohh, that works out nicely it seems.