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