Evaluate ∫ (sin x)/(cos^2 x) dx.

Indefinite Integrals · Question 14 of 90

Question 14

MediumOriginal question

Evaluate $\int \frac{\sin x}{\cos^{2} x}\,dx$ .

-\sec x + C

Correct answerYour answer

\sec x + C

Correct answerYour answer

\tan x + C

Correct answerYour answer

\sec x\tan x + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$\frac{\sin x}{\cos^{2} x} = \frac{1}{\cos x} \cdot \frac{\sin x}{\cos x} = \sec x\tan x$ .
$\int \sec x\tan x\,dx = \sec x + C$ .

Worth noting

$-\sec x$ gets the sign wrong: $\frac{d}{dx}\sec x = +\sec x\tan x$ .

Ten questions from Indefinite Integrals, at your own pace.

Ten questions from Indefinite Integrals, at your own pace.