(2 2x dx)/(( x+ x)^2) is equal to:(where C is an arbitrary constant) Option 1: (-4)/( x+ x)+C Option 2: 2 x- x +C Option 3: x+ x +C Option 4: 2 x+ x +C

Answer: 2 x+ x +C. Solution: Write 2x=( x- x)( x+ x) and cancel one factor: integrand =(2( x- x))/( x+ x). Put u= x+ x, so du=( x- x)dx, giving 2/u=2, x+ x, +C.

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$\int \frac{2\cos 2x \, dx}{(\sin x+\cos x)^2}$ is equal to:(where C is an arbitrary constant)

$\frac{-4}{\sin x+\cos x}+C$

$2\log\lvert \sin x-\cos x \rvert+C$

$\log\lvert \sin x+\cos x \rvert+C$

$2\log\lvert \sin x+\cos x \rvert+C$

✅ Correct Option: 4

Write $\cos 2x=(\cos x-\sin x)(\cos x+\sin x)$ and cancel one factor:

integrand $=\frac{2(\cos x-\sin x)}{\sin x+\cos x}$ .

Put $u=\sin x+\cos x$ , so $du=(\cos x-\sin x)dx$ , giving $2\int\frac{du}{u}=2\log|\sin x+\cos x|+C$ .

2025: 27 May Shift 1

$\int e^{-x}(\cot x + \cosec^2 x)dx =$

2024: 16 May Shift 1

The value of $\int_{0}^{1} \frac{a-b x^{2}}{\left(a+b x^{2}\right)^{2}} d x$ is :

2026: 14 May Shift 2

Match the LIST-I with LIST-II

	LIST-I (Definite integrals)		LIST-II (Value)
A.	$\displaystyle\int_{-6}^{6} \vert x \vert \, dx$	I.	$1$
B.	$\displaystyle\int_{-\pi/2}^{\pi/2} \sin^{2017} x \, dx$	II.	$36$
C.	$\displaystyle\int_{0}^{\pi/4} \cos x \, dx$	III.	$0$
D.	$\displaystyle\int_{0}^{2} \dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{2-x}} \, dx$	IV.	$\dfrac{1}{\sqrt{2}}$

Choose the correct answer from the options given below:

2025: 16 May Shift 1

$\int \frac{\cos 2x - \cos 2α}{\cos x - \cos α} dx$ is equal to

2022: 10 Aug Shift 1

$\int_0^{4\pi} \frac{x}{1 + |\cos x|} dx =$

2025: 22 May Shift 2

Match List-I with List-II (where $c$ is an arbitrary constant)

List-I	List-II
(A) $\int \tan x \, dx$	(I) $\log\vert \sec x + \tan x\vert + c$
(B) $\int \cot x \, dx$	(II) $\log\vert \sec x\vert + c$
(C) $\int \sec x \, dx$	(III) $\log\vert \sin x\vert + c$
(D) $\int \cosec x \, dx$	(IV) $\log\vert \cosec x - \cot x\vert + c$

Choose the correct answer from the options given below:

∫2cos⁡2x dx(sin⁡x+cos⁡x)2\int \frac{2\cos 2x \, dx}{(\sin x+\cos x)^2}∫(sinx+cosx)22cos2xdx​ is equal to:(where C is an arbitrary constant)

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CUET Mathematics Past Year Questions (Topic-Wise)

$\int \frac{2\cos 2x \, dx}{(\sin x+\cos x)^2}$ is equal to:(where C is an arbitrary constant)