Evaluate ∫ e^x(tan x + sec^2 x)dx.

Indefinite Integrals · Question 77 of 90

Question 77

MediumOriginal question

Evaluate $\int e^x\left(\tan x + \sec^2 x\right)dx$ .

e^x \sec^2 x + C

Correct answerYour answer

e^x\left(\tan x + \sec^2 x\right) + C

Correct answerYour answer

e^{x} \tan x + C

Correct answerYour answer

- e^{x} \tan x + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

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

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.