I know how to do this, but I'd like someone else to see if this answer is correct just for confirmation.

the indefinite integral of (5x^5 + 1)^(2/3) * 125x^4 dx

Question

I know how to do this, but I'd like someone else to see if this answer is correct just for confirmation.

the indefinite integral of (5x^5 + 1)^(2/3) * 125x^4 dx

anonymous · Answer

My answer was 12/5 (5x^5 + 1) ^ (5/3) + C

michele_laino · Answer

I got a different answer

anonymous · Answer

Okay let me walk through what I did

michele_laino · Answer

please try this substitution:
$$5{x^5} + 1 = t$$

anonymous · Answer

I set u = to 5x^5  + 1

then related that to dx with du = 25x^4dx

That left me with 4u^(2/3) dx

I said the antiderivative of that was 12/5u^(5/3)  <------ This may be the part I messed up on

Then I filled everything back in for u and added C

michele_laino · Answer

no, it is 5*u^(2/3)

anonymous · Answer

Can you explain that? I'm awful at antiderivatives

michele_laino · Answer

since 125 x^4 dx= 5 * 25x^4 dx = 5 du

michele_laino · Answer

so your  iontegrand function can be rewritten as ollows:
5 u^(2/3) du

michele_laino · Answer

and its antiderivative is:
$$5\frac{{{u^{2/3 + 1}}}}{{\frac{2}{3} + 1}} + C$$

anonymous · Answer

Oh okay so my error was in saying 4 instead of 5?

michele_laino · Answer

yes!

anonymous · Answer

Alright thank you so much. At least I'm getting the concept I think

michele_laino · Answer

thank you!