Question

Calc help for integration please!!!!!

Answer 1

Use u subsitution
the derivitive of eˣ+2 is eˣ

u=eˣ+2
du/dx=eˣ
du=eˣdx
we see a eˣdx in the problem
$\int\limits (e^x+2)^3e^x} \, dx$
sub du for that and u for eˣ+2
$\int\limits {u^3} \, du$
remember
$\int\limits {u^x} \, du= \frac{u^{x+1}}{x+1}$
$\int\limits {u^3} \, du= \frac{u^{3+1}}{3+1}= \frac{u^4}{4}$
sub eˣ+2 for u
$\frac{(e^x+2)^4}{4}$
don't forget to add a constant since the derivitive of a constant is 0

the original function is $\frac{(e^x+2)^4}{4} +C$ where C is a constant