A) \[-\frac{1}{2}\frac{1}{{{({{10}^{x}}+{{x}^{10}})}^{2}}}+c\]
B) \[\log ({{10}^{x}}+{{x}^{10}})+c\]
C) \[\frac{1}{2}\frac{1}{{{({{10}^{x}}+{{x}^{10}})}^{2}}}+c\]
D) None of these
Correct Answer: B
Solution :
Put \[{{x}^{10}}+{{10}^{x}}=t\Rightarrow (10{{x}^{9}}+{{10}^{x}}{{\log }_{e}}10)\,dx=dt,\] then \[\int_{{}}^{{}}{\frac{10{{x}^{9}}+{{10}^{x}}{{\log }_{e}}10}{{{10}^{x}}+{{x}^{10}}}\,dx}=\int_{{}}^{{}}{\frac{1}{t}\,dt=\log t+c}\] \[=\log ({{x}^{10}}+{{10}^{x}})+c.\]
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