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Question: \(\int_{}^{}{\frac{e^{5\log x}–e^{4\log x}}{e^{3\log x}–e^{2\log x}}dx}\) =...

∫e5log⁡x–e4log⁡xe3log⁡x–e2log⁡xdx\int_{}^{}{\frac{e^{5\log x}–e^{4\log x}}{e^{3\log x}–e^{2\log x}}dx} =

A

e.e–3x + c

B

e3logx + c

C

x33+c\frac{x^{3}}{3} + c

D

None

Answer

x33+c\frac{x^{3}}{3} + c

Explanation

Solution

dx = ∫x5−x4x3−x2\int \frac { x ^ { 5 } - x ^ { 4 } } { x ^ { 3 } - x ^ { 2 } } dx

= ∫x4(x−1)x2(x−1)dx\int \frac { x ^ { 4 } ( x - 1 ) } { x ^ { 2 } ( x - 1 ) } d x =