x^2 , + ,2 x^4 , + ,4 , ,dx is equal to - Vidyadip

MCQ

$\int {\frac{{{x^2}\, + \,2}}{{{x^4}\, + \,4}}} \,\,dx$ is equal to

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

✓

Answer

Correct option: D.

$\frac{1}{2}\,\,\,{\tan ^{ - 1}}\,\,\frac{{{x^2} - 2}}{{2x}}\,\, + \,\,C$

d

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