_ ^ 2x + x + 1 x^2 + 2x + 2x ;dx =

MCQ

$\int_{}^{} {\frac{{\cos 2x + x + 1}}{{{x^2} + \sin 2x + 2x}}} \;dx = $

A
$\log ({x^2} + \sin 2x + 2x) + c$
B
$ - \log ({x^2} + \sin 2x + 2x) + c$
✓
$\frac{1}{2}\log ({x^2} + \sin 2x + 2x) + c$
D
None of these

✓

Answer

Correct option: C.

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

c
(c) Put ${x^2} + \sin 2x + 2x = t,$ then it reduces to
$\frac{1}{2}\int_{}^{} {\frac{1}{t}\,dt} = \frac{1}{2}\log t + c = \frac{1}{2}\log ({x^2} + \sin 2x + 2x) + c.$

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