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  • Provide solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.8 question 22

Provide solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.8 question 22

Answers (1)

Answer:

        -\frac{a}{b}log\left | be^{-x}+c \right |+C

Hint:

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

Given:

        \int\! \! \frac{a}{b+ce^{x}}dx

Explanation:

        \int\! \! \frac{a}{e^{x}(\frac{b}{e^{x}}+c)}dx            .......(1)

        =\int\! \! \frac{ae^{-x}}{be^{-x}+c}dx

Let

        be^{-x}+c=t

        -e^{-x}(b)dx=dt

        e^{-x}dx=-\frac{1}{b}dt

Put in (1)

        \int \! \frac{a (-\frac{1}{b})dt}{t}

        =-\frac{a}{b}\int \! \frac{dt}{t}

        =-\frac{a}{b}log\left | t \right |+C

        =-\frac{a}{b}log\left | be^{-x}+c \right |+C

Posted by

Gurleen Kaur

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