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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 82 Maths Textbook Solution.

Provide Solution For  R.D.Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise  Revision Exercise Question 82 Maths Textbook Solution.

Answers (1)

Answer:

\frac{\tan ^{4} x}{4}+\frac{\tan ^{6} x}{6}+c

Hint:

You must know about the integration of tan x & sec x.

Given :

\int \tan ^{3} x \sec ^{4} x d x

Solution:

  \operatorname{let} \tan x=t, \sec ^{2} x d x=d t

\text { now, } \int \tan ^{3} x \cdot \sec ^{2} x \cdot \sec ^{2} x d x \ldots \ldots \ldots . . \text { (1) }

\text { put value of } \tan x=\operatorname{t} \text { (1) }

=\int t^{3}\left(1+\tan ^{2} x\right) \cdot \sec ^{2} x d x

=\int t^{3}\left(1+t^{2}\right) d t

=\int t^{3} d t+\int t^{5} d t

=\frac{t^{4}}{4}+\frac{t^{6}}{6}+c

=\frac{\tan ^{4} x}{4}+\frac{\tan ^{6} x}{6}+c

 

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