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Provide solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.8 question 50

Answers (1)

Answer:

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

Hint:

        U\! se\: f\! ormula\: o\! f\int \! \frac{1}{t}=log(t)+c

Given:

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

Explanation:

Let

        e^{x}+x^{e}=t

        (e^{x}+ex^{e-1})dx=dt

        e(e^{x-1}+x^{e-1})dx=dt

Put in (1)

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

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

 

 

 

Posted by

Gurleen Kaur

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