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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 80 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 80 Maths Textbook Solution.

Answers (1)

Answer:

I=\frac{\tan ^{5} x}{5}+\frac{2 \tan ^{8} x}{3}+\tan x+c

Hint:

To solve the given equation we have to split sec? x into sec? x sec² x.

Given:

\int \sec ^{6} x d x

Solution:

I=\int \sec ^{6} x d x

    =\int \sec ^{4} x \sec ^{2} x d x

    =\int\left(\sec ^{2} x\right)^{2} \sec ^{2} x d x

  \sec ^{2} x=\tan ^{2} x+1

 I=\int\left(\tan ^{2} x+1\right)^{2} \sec ^{2} x d x

 \left[\because \tan x=t \quad, \sec ^{2} x d x=d t\right.

I=\int\left(t^{2}+1\right)^{2} d t

I=\int\left(t^{4}+2 t^{2}+1\right) d t

I=\frac{t^{5}}{5}+\frac{2 t^{3}}{3}+t+c

I=\frac{\tan ^{5} x}{5}+\frac{2 \tan ^{3} x}{3}+\tan x+c

 

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