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  • Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.8 question 25 maths textbook solution

Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.8 question 25 maths textbook solution

Answers (1)

Answer:

        \frac{1}{2}log\left | e^{2x}-2 \right |+C

Hint:

       \int \frac{1}{t}dt=log\left | t \right |+C

Given:

        \int \frac{e^{2x}}{e^{2x}-2}dx                .........(1)

Explanation:

Let

        e^{2x}-2=t

        2e^{2x}dx=dt

        e^{2x}dx=\frac{dt}{2}

Put (1) we get

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

        =\frac{1}{2}log\left | t \right |+C

        =\frac{1}{2}log\left | e^{2x}-2 \right |+C

Posted by

Gurleen Kaur

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