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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{{\sin 2x}}{{1 + {{\sin }^2}x}}dx = } $
  • A
    $\log \sin 2x + c$
  • ✓
    $\log (1 + {\sin ^2}x) + c$
  • C
    $\frac{1}{2}\log (1 + {\sin ^2}x) + c$
  • D
    ${\tan ^{ - 1}}(\sin x) + c$
✓

Answer

Correct option: B.
$\log (1 + {\sin ^2}x) + c$
b
(b) Put $(1 + {\sin ^2}x) = t \Rightarrow \sin 2x\,dx = dt$
Hence $\int_{}^{} {\frac{{\sin 2x}}{{1 + {{\sin }^2}x}}dx} = \int_{}^{} {\frac{1}{t}dt = \log (1 + {{\sin }^2}x) + c.} $

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