Question

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

Answer 1

According to question,

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

$⟹\int \frac{x^6-x^5}{x^4-x^3}dx$

$⟹\int \frac{x^5(x-1)}{x^3(x-1)}dx$

$⟹\int x^{2}dx$

$⟹\frac{x^3}{3}+C$