A) \[{{(3)}^{{{x}^{3}}}}+c\]
B) \[\frac{{{(3)}^{{{x}^{3}}}}}{\log 3}+c\]
C) \[\log 3{{(3)}^{{{x}^{3}}}}+c\]
D) None of these
Correct Answer: B
Solution :
\[\int_{{}}^{{}}{{{x}^{2}}{{(3)}^{{{x}^{3}}+1}}dx}=\int_{{}}^{{}}{3{{x}^{2}}.\,{{(3)}^{{{x}^{3}}}}dx}\] Putting \[{{x}^{3}}=t\Rightarrow 3{{x}^{2}}\,dx=dt,\] we get \[=\int_{{}}^{{}}{{{3}^{t}}dt=\frac{{{3}^{t}}}{\log 3}+c=\frac{{{(3)}^{{{x}^{3}}}}}{\log 3}+c}\].
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