Q63 / 150 · MHT CET 2020 (15 Oct Shift 1) · Mathematics

$\int \frac{d x}{\cos 2 x+\sin ^{2} x}=$

  • A
    $\sin x+c$
  • Correct answer
    B
    $\tan x+c$
  • C
    $\sec ^{2} x+c$
  • D
    $\cos x+c$

Solution

$\begin{aligned} I &=\int \frac{d x}{1-2 \sin ^{2} x+\sin ^{2} x} \\ &=\int \frac{d x}{1-\sin ^{2} x}=\int \frac{d x}{\cos ^{2} x}=\int \sec ^{2} x d x=\tan x+c \end{aligned}$

Hence, the correct answer is option: 'B'.

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