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  • Provide solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.8 question 46

Provide solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.8 question 46

Answers (1)

Answer:

        2log\left | \sqrt{x}+1 \right |+C

Hint:

        Let \sqrt{x}=t

Given:

        \int \! \frac{1}{\sqrt{x}(\sqrt{x}+1)}dx                        .......(1)

Explanation:

Let

        \sqrt{x}=t

        \frac{1}{2\sqrt{x}}dx=dt

        \frac{dx}{\sqrt{x}}=2dt

From (1) we have

        \int \! \frac{2dt}{t+1}=2\int \! \frac{1}{t+1}dt

        =2log\left | t+1 \right |

        =2log\left | \sqrt{x}+1 \right |+C

Posted by

Gurleen Kaur

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