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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int {{e^{3\log x}}{{({x^4} + 1)}^{ - 1}}\,\,dx} $=
  • A
    $\log ({x^4} + 1) + c$
  • ✓
    $\frac{1}{4}\log ({x^4} + 1) + c$
  • C
    $ - \log ({x^4} + 1) + c$
  • D
    None of these
✓

Answer

Correct option: B.
$\frac{1}{4}\log ({x^4} + 1) + c$
b
(b) $I = \int {{e^{3\log x}}{{({x^4} + 1)}^{ - 1}}dx} $$ = \int {{e^{\log {x^3}}}{{({x^4} + 1)}^{ - 1}}dx} $
$ = \frac{1}{4}\int {\frac{{4{x^3}}}{{({x^4} + 1)}}dx} = \frac{1}{4}\log ({x^4} + 1) + c$.

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