_ ^ a^ 3x + 3 dx = - Vidyadip

MCQ

$\int_{}^{} {{a^{3x + 3}}dx} = $

A
$\frac{{{a^{3x + 3}}}}{{\log a}} + c$
✓
$\frac{{{a^{3x + 3}}}}{{3\log a}} + c$
C
${a^{3x + 3}}\log a + c$
D
$3{a^{3x + 3}}\log a + c$

✓

Answer

Correct option: B.

$\frac{{{a^{3x + 3}}}}{{3\log a}} + c$

b
(b) 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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