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  • need solution for rd sharma maths class 12 chapter Indefinite integrals exercise 18.1 question 4

need solution for rd sharma maths class 12 chapter Indefinite integrals exercise 18.1 question 4

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Answer: \frac{a^{-x}b^{-x}}{-\log_{e}\left ( ab \right )}+c

Hint: You must know the formula of \int a^{x}dx

Given: \int \frac{1}{a^{x}b^{x}}dx

Solution: \int \frac{1}{a^{x}b^{x}}dx

=\int a^{-x}b^{-x}dx=\int \left ( ab \right )^{-x}dx

=\frac{\left ( ab \right )^{-x}}{\log_{e}\left ( ab \right )^{-1}}                                    \left ( \because \int a^{x}dx=\frac{a^{x}}{\log a} \right )

=\frac{a^{-x}b^{-x}}{-\log_{e}\left ( ab \right )}+c

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