Evaluate ∫ e^x(1/x - 1/x^2)dx.

Indefinite Integrals · Question 81 of 90

Question 81

MediumOriginal question

Evaluate $\int e^{x}\left(\frac{1}{x} - \frac{1}{x^{2}}\right)dx$ .

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

Correct answerYour answer

e^{x}\log x + C

Correct answerYour answer

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

Correct answerYour answer

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

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

This is $e^{x}\left(f(x) + f'(x)\right)$ with $f(x) = \frac{1}{x}$ , since $f'(x) = -\frac{1}{x^{2}}$ .
$\int e^{x}(f + f')\,dx = e^{x}f(x) + C = \frac{e^{x}}{x} + C$ .

Worth noting

$-\frac{e^{x}}{x^{2}}$ picks $f'$ as the function; it must be $f$ , the part whose derivative is also there.

Ten questions from Indefinite Integrals, at your own pace.

Ten questions from Indefinite Integrals, at your own pace.