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  • Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 31 Maths Textbbok Solution.

Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise  Revision Exercise Question 31 Maths Textbbok Solution.

Answers (1)

Answer:

-\frac{1}{3} \cot ^{3} x+\cot x+x+c

Given:

\int \cot ^{4} x d x

Hint:

To solve the given statement split the given term \left(\cot ^{4} x\right) into \left(\cot ^{2} x \cot ^{2} x\right)

Solution: 

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

    I=\int \cot ^{2} x \operatorname{cosec}^{2} x d x-\int \cot ^{2} d x                        

    I=\int \cot ^{2} x \operatorname{cosec}^{2} x d x-\int\left(\operatorname{cosec}^{2} x-1\right) d x                                \left[\because \cot x=p, \operatorname{cosec}^{2} x d x=-d p\right.

    I=-\int p^{2} d p+\int d p+\int d x

    I=-\frac{p^{8}}{3}+p+x+c

    I=-\frac{1}{3} \cot ^{3} x+\cot x+x+c

 

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