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  • Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 71 Maths Textbbok Solution.

Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise  Revision Exercise Question 71 Maths Textbbok Solution.

Answers (1)

Answer:

-\frac{\cot 2 x}{2}-\frac{\cot ^{8} 2 x}{6}+c

Hint:

To solve the given question we will split the cosec? 2x into cosec² 2x cosec² 2x.

Given:

\int \operatorname{cosec}^{4} 2 x d x

Solution:

=\int \operatorname{cosec}^{4} 2 x d x

=\int \operatorname{cosec}^{2} 2 x \operatorname{cosec}^{2} 2 x d x

=\int\left(1+\cot ^{2} 2 x\right) \operatorname{cosec}^{2} 2 x d x

p u t \cot 2 x=t=>-\operatorname{cosec}^{2} 2 x \cdot 2 d x=d t

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

=-\frac{1}{2} t-\frac{t^{3}}{6}+c

=-\frac{\cot 2 x}{2}-\frac{\cot ^{3} 2 x}{6}+c

 

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