Mathematics

Solve $$\displaystyle\int { \dfrac { { e }^{ 6\log { x }  }-{ e }^{ 5\log { x }  } }{ { e }^{ 4\log { x }  }-{ e }^{ 3\log { x }  } }  } dx$$


SOLUTION
According to question,

$$\int \dfrac{e^{6\ logx}-e^{5\ logx}}{e^{4\ logx}-e^{3\ logx}}dx$$

$$\implies \int \dfrac{x^6-x^5}{x^4-x^3}dx$$

$$\implies \int \dfrac{x^5(x-1)}{x^3(x-1)}dx$$

$$\implies \int x^2dx$$

$$\implies \dfrac{x^3}{3}+C$$
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Subjective Medium Published on 17th 09, 2020
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