Question

Integrate 8 tan^3⁡x sec^2⁡x.

(a) 2 tan^4⁡x+C

(b) 4 cot^4⁡x+C

(c) 2 tan^3⁡x+C

(d) tan^4⁡x+C

This question was addressed to me in final exam.

Query is from Methods of Integration-2 topic in portion Integrals of Mathematics – Class 12

Answer 1

Correct option is (a) 2 tan^4⁡x+C

The explanation: To find: \(\int 8 \,tan^3⁡x \,sec^2⁡x \,dx\)

Let tan⁡x=t

sec^2⁡x dx=dt

∴\(\int 8 \,tan^3⁡x \,sec^2⁡x \,dx=\int 8 \,t^3 \,dt=\frac{8t^4}{4}=2t^4\)

Replacing t with tan⁡x, we get

\(\int 8 tan^3⁡x sec^2⁡x dx=2 tan^4⁡x+C\)