Question

indefinite integral problem

Answer 1

\[\int\limits_{?}^{?} (x^2+1) (x^3+3x)^4 dx\]

Answer 2

this is what i have so far u=x^(3)+3x and du/3x^(2)+3=dx

Answer 3

Substitute \(u=x^3+3x\), so that \(du=(3x^2+3)~dx\), i.e. \(\dfrac{1}{3}du=(x^2+1)~dx\).
\[\int (x^2+1)(x^3+3x)^4~dx=\frac{1}{3}\int u^4~du\]
Yep you've got it.

Answer 4

but i have problem with the plug in part