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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 79 Maths Textbook Solution.

Provide Solution For R.D. Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise  Revision Exercise Question 79 Maths Textbook Solution.

Answers (1)

Answer:

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

Hint:

To solve the given statement divide the numerator and denominator by cos²x.

Given:

=\int \frac{\sin ^{2} x}{\cos ^{6} x} d x

Solution: 

=\int \frac{\frac{\sin ^{2} x}{\cos ^{2} x}}{\frac{\cos ^{6} x}{\cos ^{2} x}} d x

=\int \tan ^{2} x \sec ^{4} x d x

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

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

=\int t^{2} d t+\int t^{4} d t

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

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

 

 

Posted by

infoexpert21

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