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Need solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.8 question 35

Answers (1)

Answer:

        log\left | 10^{x}+x^{10} \right |+C

Hint:

        \frac{\mathrm{d} }{\mathrm{d} x}(10^{x}+x^{10})=10x^{9}+10^{x}log_{e}10

Given:

        \int \! \frac{10x^{9}+10^{x}log_{e}10}{10^{x}+x^{10}}dx                .......(1)

Explanation:

Let

        10^{x}+x^{10}=t

        (10x^{9}+10^{x}log_{e}10)dx=dt

From (1) we get

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

        =log\left | 10^{x}+x^{10} \right |+C

Posted by

Gurleen Kaur

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