A) \[e\ .\ {{3}^{-3x}}+c\]
B) \[{{e}^{3}}\log x+c\]
C) \[\frac{{{x}^{3}}}{3}+c\]
D) None of these
Correct Answer: C
Solution :
\[\int_{{}}^{{}}{\frac{{{e}^{5\log x}}-{{e}^{4\log x}}}{{{e}^{3\log x}}-{{e}^{2\log x}}}\,dx}=\int_{{}}^{{}}{\frac{{{x}^{5}}-{{x}^{4}}}{{{x}^{3}}-{{x}^{2}}}\,dx}\] \[=\int_{{}}^{{}}{\frac{{{x}^{4}}(x-1)}{{{x}^{2}}(x-1)}\,dx}=\int_{{}}^{{}}{{{x}^{2}}dx}=\frac{{{x}^{3}}}{3}+c\].
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