Evaluate ∫ x e^x^2 dx.

Question 21

MediumOriginal question

Evaluate $\int x e^{x^{2}}\,dx$ .

e^{x^{2}} + C

Correct answerYour answer

- \frac{e^{x^{2}}}{2} + C

Correct answerYour answer

x^{2} e^{x^{2}} + C

Correct answerYour answer

\frac{e^{x^{2}}}{2} + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Put $t = x^2$ ; then $dt$ is the rest of the integrand, up to a constant.
The integral becomes a standard form in $t$ ; putting $t = x^2$ back gives $\frac{e^{x^{2}}}{2} + C$ .
Check: differentiating the answer gives back the integrand.

Worth noting

Getting the constant from $dt$ wrong multiplies or divides the answer: check by differentiating.

Ten questions from Indefinite Integrals, at your own pace.