Integrate 8 tan^3⁡x sec^2⁡x.

Category: QuestionsIntegrate 8 tan^3⁡x sec^2⁡x.
Editor">Editor Staff asked 11 months ago

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
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

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