Question

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

• A. $e.3^{-3x}$
• B. $e^3.\log x$
• C. $\frac{x^3}{3}$
• D. $\frac{x^2}{2}$

Answer 1

Answer: (C)

$\frac{x^3}{3}$

$e^{klogx}=e^{\log x^k}=x^k$

Now , in question-

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

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

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

$=\int x^{2}dx$

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