Evaluate ∫ e^x(x^2 + 2x)dx.

Indefinite Integrals · Question 79 of 90

Question 79

MediumOriginal question

Evaluate $\int e^x\left(x^{2} + 2x\right)dx$ .

e^x 2x + C

Correct answerYour answer

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

Correct answerYour answer

e^x\left(x^{2} + 2x\right) + C

Correct answerYour answer

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

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$\int e^x\left(f(x) + f'(x)\right)dx = e^x f(x) + C$ , because $\frac{d}{dx}\left(e^x f(x)\right) = e^x\left(f(x) + f'(x)\right)$ .
Here $f(x) = x^{2}$ and $f'(x) = 2x$ , so the integral is $x^{2} e^{x} + C$ .

Worth noting

The function that goes with $e^x$ is the one whose derivative is the other term.

Ten questions from Indefinite Integrals, at your own pace.

Ten questions from Indefinite Integrals, at your own pace.