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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
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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