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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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