A) \[\frac{{{a}^{3x+3}}}{\log a}+c\]
B) \[\frac{{{a}^{3x+3}}}{3\log a}+c\]
C) \[{{a}^{3x+3}}\log a+c\]
D) \[3{{a}^{3x+3}}\log a+c\]
Correct Answer: B
Solution :
Put \[t=3x+3\Rightarrow dt=3\,dx,\] then \[\int_{{}}^{{}}{{{a}^{3x+3}}dx}=\frac{1}{3}\int_{{}}^{{}}{{{a}^{t}}dt}=\frac{1}{3}\frac{{{a}^{t}}}{{{\log }_{e}}a}+c=\frac{{{a}^{3x+3}}}{3{{\log }_{e}}a}+c\].
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