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Indefinite Integrals · Question 30 of 90

Question 30

MediumOriginal question

Evaluate ∫tan⁡3xsec⁡2x dx\int \tan^{3} x\sec^{2} x\,dx.

Options for question 30

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. Put t=tan⁡xt = \tan x, dt=sec⁡2x dxdt = \sec^{2} x\,dx.

  2. ∫t3 dt=t44=tan⁡4x4+C\int t^{3}\,dt = \frac{t^{4}}{4} = \frac{\tan^{4} x}{4} + C.

Worth noting

tan⁡4xsec⁡3x12\frac{\tan^{4} x\sec^{3} x}{12} integrates the two factors separately and multiplies, which is not how integrals work.

Concept
Integration by substitution
Typical time
90 s
Your time
—
The rule this testsIntegration by substitution
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Ten questions from Indefinite Integrals, at your own pace.

Practise this chapter →

Ten questions from Indefinite Integrals, at your own pace.