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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 103 Maths Textbook Solution.

Provide Solution For  R.D.Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise  Revision Exercise Question 103  Maths Textbook Solution.

Answers (1)

Answer: \frac{2}{9}\left(1+x^{3}\right)^{3 / 2}-\frac{2}{3} \sqrt{1+x^{3}}+c

Hint: to solve this question we have to use substitute method

Given:  \int \frac{x^{5}}{\sqrt{1+x^{3}}} d x

Solution:

\text { Let } I=\int \frac{x^{3} \cdot x^{2}}{\sqrt{1+x^{3}}} d x

\text { put } 1+x^{3}=t^{2}, \text { differentiate on both sides, }

3 x^{2} d x=2 t d t

I=\int \frac{\left(t^{2}-1\right)}{t} \cdot \frac{2 t d t}{3}

I=\frac{2}{3} \int\left(t^{2}-1\right) d t

I=\frac{2}{3} \int t^{2} d t-\frac{2}{3} \int d t

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

I=\frac{2}{9}\left(\sqrt{1+x^{3}}\right)^{3}-\frac{2}{3} \sqrt{1+x^{3}}+c

I=\frac{2}{9}\left(1+x^{3}\right)^{3 / 2}-\frac{2}{3} \sqrt{1+x^{3}}+c

 

 

 

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