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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 53 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 53 Maths Textbook Solution.

Answers (1)

Answer:

I=\left[\sqrt{x^{2}+x}+\ln (\sqrt{x}+\sqrt{x+1})\right]+c

 

ùTo solve this equation we have to take x = u².

Solution: 

I=\int \sqrt{\frac{(x+1)}{x}} \mathrm{dx}

\text { Let } x=u^{2}

d x=2 u d u

I=\int \sqrt{\frac{\left(u^{2}+1\right)}{\mathrm{u}^{2}}} 2 \mathrm{udu}

 

I=\int 2 \sqrt{u^{2}+1} d u                            \left[\because \int \sqrt{x^{2}+a^{2}}=\frac{x}{2} \sqrt{x^{2}+a^{2}}+\frac{a^{2}}{2} \ln x+\sqrt{x^{2}+a^{2}}+c\right]

I=2\left[\frac{u}{2} \sqrt{u^{2}+1}+\frac{1}{2} \ln \left(u+\sqrt{u^{2}+1}\right)\right]+c

I=2\left[\frac{\sqrt{x}}{2} \sqrt{x+1}+\frac{1}{2} \ln (\sqrt{x}+\sqrt{x+1})\right]+c

I=\left[\sqrt{x^{2}+x}+\ln (\sqrt{x}+\sqrt{x+1})\right]+c

 

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