Mathematics

The value of the integral $$\displaystyle \int \frac{e^{7\log x} - e^{6\log x}}{e^{5\log x} - e^{4 \log x}} dx$$ is equal to


ANSWER

$$\displaystyle \frac{x^{3}}{3}+c$$


SOLUTION
$$\displaystyle\int  \dfrac { e^{ 7\log  x }-e^{ 6\log  x } }{ e^{ 5\log  x }-e^{ 4\log  x } } dx=\int { \cfrac { { x }^{ 7 }-{ x }^{ 6 } }{ { x }^{ 5 }-{ x }^{ 4 } } dx }\displaystyle=\int { { x }^{ 2 }dx } =\cfrac { { x }^{ 3 } }{ 3 } +c$$
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Single Correct Medium Published on 17th 09, 2020
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