Question

do i have to use u-substitution to integrate e^xsqrt(8 + e^x) ? i dont know if i have to do that or just use product rule. what is general rule of thumb for u-sub?

Answer 1

Hint:

let u = 8+e^x

derive to get du/dx = e^x

that turns into

du = dx*e^x

Answer 2

so...

e^xsqrt(8 + e^x) dx

turns into

(dx*e^x)sqrt(8 + e^x)

which turns into

du*sqrt(u)

Answer 3

ah yeah you can get rid of the other e^x if you do it that way. i have no idea why i have so much trouble with this but thank you!