A) \[\frac{1}{x}{{e}^{x}}+c\]
B) \[x{{e}^{-x}}+c\]
C) \[\frac{1}{{{x}^{2}}}{{e}^{x}}+c\]
D) \[\left( x-\frac{1}{x} \right){{e}^{x}}+c\]
Correct Answer: A
Solution :
\[\int_{{}}^{{}}{\frac{{{e}^{x}}(x-1)}{{{x}^{2}}}\,dx}=\int_{{}}^{{}}{{{e}^{x}}\left[ \frac{1}{x}-\frac{1}{{{x}^{2}}} \right]}\,dx=\frac{{{e}^{x}}}{x}+c.\]You need to login to perform this action.
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