Evaluate ∫ tan x dx.

Question 22

MediumOriginal question

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

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

Correct answerYour answer

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

Correct answerYour answer

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

Correct answerYour answer

x \tan x + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Put $t = \cos x$ ; then $dt$ is the rest of the integrand, up to a constant.
The integral becomes a standard form in $t$ ; putting $t = \cos x$ back gives $\log\left|\sec x\right| + C$ .
Check: differentiating the answer gives back the integrand.

Worth noting

Getting the constant from $dt$ wrong multiplies or divides the answer: check by differentiating.

Ten questions from Indefinite Integrals, at your own pace.