dx/(^2 x ^2 x) = Option 1: x + x + C Option 2: x - x + C Option 3: x x + C Option 4: x - 2x + C

Answer: x - x + C. Solution: 1/(^2 x ^2 x) = (^2 x + ^2 x)/(^2 x ^2 x) = ^2 x + ^2 x. Integrating: x - x + C.

Calculus

Integrals

Easy

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

$\tan x + \cot x + C$

$\tan x - \cot x + C$

$\tan x \cot x + C$

$\tan x - \cot 2x + C$

✅ Correct Option: 2

$\frac{1}{\sin^2 x \cos^2 x} = \frac{\sin^2 x + \cos^2 x}{\sin^2 x \cos^2 x} = \sec^2 x + \csc^2 x$ . Integrating: $\tan x - \cot x + C$ .

2026: 15 May Shift 1

If $\displaystyle\int_0^3 (8x^3+5x^2-2x-k)\,dx = 3$ , where $k$ is constant, then $k$ is equal to

2022: 7 Aug Shift 2

$\int \frac{1}{\cos^2 x (1 + \tan x)^3} \, dx =$

2023: 22 May Shift 3

$\int_1^2 \frac{x \, dx}{(x+1)(x+2)} =$

2025: 19 May Shift 1

Value of $\int \frac{2}{(x-3)\sqrt{x+1}} dx$ is: (Here C is an arbitrary constant)

2026: 12 May Shift 2

The value of $\displaystyle\int_{-1}^{1}|x^4-x|\,dx$ is equal to:

2022: 16 July Shift 2

$\int \frac{x^2+1}{(x+1)^2} e^x \, dx$ is equal to