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  • Integrate the functions in Exercises 1 to 24. 8

Integrate the functions in Exercises 1 to 24.

    Q8.    \frac{e^{5\log x} - e^{4\log x}}{e^{3\log x}-e^{2\log x}}

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Simplifying the equation we get, 

                              \frac{e^{5\log x} - e^{4\log x}}{e^{3\log x}-e^{2\log x}}\ =\ \frac {e^{4\log x}}{e^{2\log x}}\times \frac{e^{\log x} - 1}{e^{\log x}-1}

or                                                              =\ e^{2\log x}\ =\ x^2

Thus it becomes :

                                         \int \frac{e^{5\log x} - e^{4\log x}}{e^{3\log x}-e^{2\log x}}dx\ =\ \int e^{2\log x}dx

                                                                                        =\ \int x^2dx

                                                                                        =\ \frac{x^3}{3}\ +\ C

 

Posted by

Devendra Khairwa

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