_ ^ e^ 5 x - e^ 4 x e^ 3 x - e^ 2 x ;dx = - Vidyadip

MCQ

$\int_{}^{} {\frac{{{e^{5\log x}} - {e^{4\log x}}}}{{{e^{3\log x}} - {e^{2\log x}}}}\;dx = } $

A
$e\;.\;{3^{ - 3x}} + c$
B
${e^3}\log x + c$
✓
$\frac{{{x^3}}}{3} + c$
D
None of these

✓

Answer

Correct option: C.

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

c
(c)$\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$.

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