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Indefinite Integrals · Question 34 of 90

Question 34

EasyOriginal question

Evaluate ∫tan⁡2x dx\int \tan^{2} x\,dx.

Options for question 34

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. Rewrite first: tan⁡2x=sec⁡2x−1\tan^2 x = \sec^2 x - 1.

  2. Then each term is standard: tan⁡x−x+C\tan x - x + C.

  3. Check: differentiating the answer gives back the integrand.

Worth noting

A power of a trig function has no direct standard form: the identity is what makes it integrable.

Concept
Integrating tan² x
Typical time
60 s
Your time
—
The rule this testsIntegration with trigonometric identities
Practise this chapter →

Ten questions from Indefinite Integrals, at your own pace.

Practise this chapter →

Ten questions from Indefinite Integrals, at your own pace.