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STD 12 - 7.1 inderfinite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.1 inderfinite integral1 Mark
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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