Evaluate ∫ (3 e^x + 4/x) dx.

Question 3

EasyOriginal question

Evaluate $\int \left(3 e^{x} + \frac{4}{x}\right)\,dx$ .

3 e^{x} + 4 \log\left|x\right| + C

Correct answerYour answer

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

Correct answerYour answer

3 x e^{x} + 4 + C

Correct answerYour answer

- 3 e^{x} - 4 \log\left|x\right| + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Integrate term by term with the standard forms: $\int x^n\,dx = \frac{x^{n+1}}{n+1}$ , $\int \frac{1}{x}\,dx = \log|x|$ , $\int e^x\,dx = e^x$ .
$\int \left(3 e^{x} + \frac{4}{x}\right)\,dx = 3 e^{x} + 4 \log\left|x\right| + C$ .
Check: differentiating the answer gives back the integrand.

Worth noting

$3 e^{x} - \frac{4}{x^{2}}$ differentiates instead of integrating.

Ten questions from Indefinite Integrals, at your own pace.