Question

find the integral of xe^(x^2) with respect to x

Answer 1

u=x^2

Answer 2

hmm i was trying that but it wasnt working out

Answer 3

\[\Large \int\limits_{ }^{ }xe^{x^2}~dx\]
\(\large\color{black}{u=x^2 }\)

\(\large\color{black}{\frac{du}{dx}(x^2)=2x }\)

So, the du = (derivative of u) times dx
du = 2x times dx

Answer 4

Your du=2x dx has to modified, since you only got x inside the integral, not to x, so lets go ahead an divide both sides by 2, we get,
\(\large\color{black}{ \frac{1}{2}du =x ~dx }\)

Answer 5

So, your subs are:
\(\large\color{black}{ u=x^2 }\) and \(\large\color{black}{ \frac{1}{2}du =x ~dx }\) .

Answer 6

and that would get rid of the x in front of the e^(x^2) right

Answer 7

You might want to just take a minute to take the derivative a similar function if you're unsure of its integral since usually it will follow a similar pattern.

\[\LARGE (e^{x^2})'=2xe^{x^2}\]
So you can see that if you divide both sides by 2 and integrate both sides you will have the answer to your integral:
\[\LARGE \int \frac{1}{2}(e^{x^2})' dx=\int xe^{x^2}dx\]
\[\LARGE \frac{1}{2}e^{x^2} +C=\int xe^{x^2}dx\]

Answer 8

yes, @YadielG

Answer 9

ok awesome thanks because the part that had me confused is that i was doing du/2x instead of keeping the x with the dx

Answer 10

kainui, testing integral by where it came from is a good thing, but I think the user is asked to show the work, not to guess what the derivative that it is coming from....

Answer 11

Yes, so what do you get after substitution?

Answer 12

(1/2) e^(x^2)

Answer 13

that should be right

Answer 14

you substitute x^2 with u?

Answer 15

thank you very much sir

Answer 16

and yes i did