e^ 3 x ( x^4 + 1) ^ - 1 , ,dx =

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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