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