Evaluate ∫ sec x dx.

Indefinite Integrals · Question 27 of 90

Question 27

MediumOriginal question

Evaluate $\int \sec x\,dx$ .

\sec x\tan x + C

Correct answerYour answer

\log\left|\sec x + \tan x\right| + C

Correct answerYour answer

\log\left|\sec x - \tan x\right| + C

Correct answerYour answer

\log\left|\cos x\right| + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Multiply top and bottom by $\sec x + \tan x$ : $\int \frac{\sec^{2} x + \sec x\tan x}{\sec x + \tan x}\,dx$ .
The top is now the derivative of the bottom, so the integral is $\log|\sec x + \tan x| + C$ .

Worth noting

$\sec x\tan x$ is the derivative of $\sec x$ , not its integral.

Ten questions from Indefinite Integrals, at your own pace.

Ten questions from Indefinite Integrals, at your own pace.