∫ c o s 2 x + s i n 2 x d x =, sin x + c, tan x + c, sec 2 x + c, cos x + c

I = ∫ 1 − 2 sin 2 x + sin 2 x d x = ∫ 1 − sin 2 x d x = ∫ cos 2 x d x = ∫ sec 2 x d x = tan x + c

∫ c o s 2 x + s i n 2 x d x =

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Question: Answered & Verified by Expert

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

MathematicsIndefinite IntegrationMHT CETMHT CET 2020 (15 Oct Shift 1)

Options:

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

Solution:

2550 Upvotes Verified Answer

The correct answer is: $\tan x+c$

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

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