Question

Which of the following integrals cannot be evaluated using a simple substitution?

Answer 1

any guesses?
two have a very obvious substitution

Answer 2

and one cannot be evaluated at all

Answer 3

\[\int xe^{x^2}dx\] put \(u=x^2, du = 2xdx\) so \(\frac{1}{2}du=dx\) evaluate \[\frac{1}{2}\int e^udu\] in your head

Answer 4

it works because \(x\) looks like the derivative of \(x^2\)
only off by a two

Answer 5

wait what? it's off by two?

Answer 6

\[\int xe^{x^2}dx=\int e^x\color{red}{xdx}\] and here \(\color{red}{xdx}\) is almost \(\color{red}{du}\) since if \(u=x^2\) then \(\color{red}{du}=2\color{red}{xdx}\)

Answer 7

typo there i meant \[\int xe^{x^2}dx=\int e^{x^2}\color{red}{xdx}\]

Answer 8

oohh okay. Well then it's either c or d