Integral Calculus Question 418
Question: $ \int_{{}}^{{}}{x^{2}{{(3)}^{x^{3}+1}}dx=} $
Options:
A) $ {{(3)}^{x^{3}}}+c $
B) $ \frac{{{(3)}^{x^{3}}}}{\log 3}+c $
C) $ \log 3{{(3)}^{x^{3}}}+c $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \int_{{}}^{{}}{x^{2}{{(3)}^{x^{3}+1}}dx}=\int_{{}}^{{}}{3x^{2}.,{{(3)}^{x^{3}}}dx} $ Putting $ x^{3}=t\Rightarrow 3x^{2},dx=dt, $ we get $ =\int_{{}}^{{}}{3^{t}dt=\frac{3^{t}}{\log 3}+c=\frac{{{(3)}^{x^{3}}}}{\log 3}+c} $ .
BETA
