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Indefinite Integrals · Question 19 of 90

Question 19

EasyOriginal question

Evaluate ∫cot⁡x dx\int \cot x\,dx.

Options for question 19

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. cot⁡x=cos⁡xsin⁡x\cot x = \frac{\cos x}{\sin x}: the top is the derivative of the bottom.

  2. So ∫cot⁡x dx=log⁡∣sin⁡x∣+C\int \cot x\,dx = \log|\sin x| + C.

Worth noting

−log⁡∣sin⁡x∣-\log|\sin x| mixes it up with ∫tan⁡x dx=−log⁡∣cos⁡x∣\int \tan x\,dx = -\log|\cos x|, which does carry a minus.

Concept
The integral of cot x
Typical time
60 s
Your time
—
The rule this testsIntegration by substitution
Practise this chapter →

Ten questions from Indefinite Integrals, at your own pace.

Practise this chapter →

Ten questions from Indefinite Integrals, at your own pace.