# Should this be $\int u^2 \sqrt{u+1} du$ after substitution of $u=e^x$?

Should this be $\int u^2 \sqrt{u+1} du$ after substitution of $u=e^x$? http://www.wolframalpha.com/input/?i=integrate+%28exp%28x%29%29^2*sqrt%281%2Bexp%28x%29%29 -> show steps ->3rd row

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No, when you do the substitution $u=e^x$ then $du=e^x dx$ so $dx=du/u$ which is why it's $u$ and not $u^2$.