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

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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