{e^{5 x}-e^{4 x}}{e³ x}-e² x}} - NCERT Class XII Mathematics ...

NCERT Class XII Mathematics Chapter - - Solutions

..... Miscellaneous Exercise .....
Integrate the functions in Exercises 229 to 252.

Question : 236 of 271

Marks: +1, -0

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

Solution:

Let

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

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

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

=\int \frac{x^4(x-1)}{x^2(x-1)} dx

=\int x^2 \, dx = \frac{x^3}{3}+C

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