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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 61 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 61 Maths Textbook Solution.

Answers (1)

Answer:

I=\frac{1}{4} \ln \left|x^{4}+\sqrt{x^{8}+4}\right|+c

Hint :

 To solve this given statement split the x? term to (x?)² then put x? equal to t.

Given:

\int \frac{x^{8}}{\sqrt{x^{8}+4}} d x

Solution:

I=\int \frac{x^{8}}{\sqrt{x^{8}+4}} d x

  I=\int \frac{x^{3}}{\sqrt{\left(x^{4}\right)^{2}+4}} d x

I=\int \frac{\frac{1}{4} d t}{\sqrt{t^{2}+4}}                                                    \left[\because x^{4}=t, d t=4 x^{3} d x, x^{3} d x=\frac{d t}{4}\right]

I=\frac{1}{4} \int \frac{d t}{\sqrt{t^{2}+2^{2}}}

I=\frac{1}{4} \ln \left|t+\sqrt{t^{2}+4}\right|+c

I=\frac{1}{4} \ln \left|x^{4}+\sqrt{x^{8}+4}\right|+c

 

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infoexpert21

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