_ ^ 1 x - x^3 ;dx = - Vidyadip

MCQ

$\int_{}^{} {\frac{1}{{x - {x^3}}}\;dx = } $

A
$\frac{1}{2}\log \frac{{(1 - {x^2})}}{{{x^2}}} + c$
B
$\log \frac{{(1 - x)}}{{x(1 + x)}} + c$
C
$\log x(1 - {x^2}) + c$
✓
$\frac{1}{2}\log \frac{{{x^2}}}{{(1 - {x^2})}} + c$

✓

Answer

Correct option: D.

$\frac{1}{2}\log \frac{{{x^2}}}{{(1 - {x^2})}} + c$

d
(d)$\int_{}^{} {\frac{1}{{x - {x^3}}}\,dx = \int_{}^{} {\frac{1}{{x(1 + x)(1 - x)}}\,dx} } $
$ = \frac{1}{2}\int_{}^{} {\left( {\frac{2}{x} - \frac{1}{{1 + x}} + \frac{1}{{1 - x}}} \right)\,dx} $
$ = \frac{1}{2}[2\log x - \log (1 + x) - \log (1 - x)] = \frac{1}{2}\log \frac{{{x^2}}}{{(1 - {x^2})}} + c$.

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