Evaluate ∫ xe^2x dx.

Indefinite Integrals · Question 84 of 90

Question 84

MediumOriginal question

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

\frac{xe^{2x}}{2} + \frac{e^{2x}}{4} + C

Correct answerYour answer

\frac{xe^{2x}}{2} - \frac{e^{2x}}{4} + C

Correct answerYour answer

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

Correct answerYour answer

\frac{x^{2}e^{2x}}{4} + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$u = x$ , $dv = e^{2x}\,dx$ : $v = \frac{e^{2x}}{2}$ .
$\frac{xe^{2x}}{2} - \int \frac{e^{2x}}{2}\,dx = \frac{xe^{2x}}{2} - \frac{e^{2x}}{4} + C$ .

Worth noting

$+\frac{e^{2x}}{4}$ adds what by parts subtracts: $\int u\,dv = uv - \int v\,du$ .

Ten questions from Indefinite Integrals, at your own pace.

Ten questions from Indefinite Integrals, at your own pace.