If (1 + x x)/(xe^(-x)) dx = e^x f(x) + C, where C is constant of integration, then f(x) is Option 1: e^x Option 2: x Option 3: 1/x Option 4: 1/x^2

Answer: x. Solution: Solution Coming Soon

Calculus

Integrals

Hard

applied

If $\int \frac{(1 + x \log x)}{xe^{-x}} dx = e^x f(x) + C$ , where C is constant of integration, then $f(x)$ is

$e^x$

$\log x$

$\frac{1}{x}$

$\frac{1}{x^2}$

✅ Correct Option: 2

Solution Coming Soon

2026: 14 May Shift 2

If C is an arbitrary constant, then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\displaystyle\int a^x \, dx$	I.	$\sin^{-1}\dfrac{x}{a} + C$
B.	$\displaystyle\int \dfrac{dx}{\sqrt{a^2 - x^2}}$	II.	$\log_e \vert x + \sqrt{x^2 - a^2} \vert + C$
C.	$\displaystyle\int \dfrac{dx}{\sqrt{a^2 + x^2}}$	III.	$\dfrac{a^x}{\log_e a} + C$
D.	$\displaystyle\int \dfrac{dx}{\sqrt{x^2 - a^2}}$	IV.	$\log_e \vert x + \sqrt{a^2 + x^2} \vert + C$

Choose the correct answer from the options given below:

2022: 10 Aug Shift 1

$\int_0^1 \frac{dx}{x^2 + x + 1}$

2025: 19 May Shift 1

If $2f(x) + f\left(\frac{1}{x}\right) = x^2 + 1$ , then $\int f(x) dx$ is: (Here C is an arbitrary constant)

2025: 13 May Shift 1

$\int \sin x \sin 2x \sin 3x dx$ is equal to

2026: 26 May Shift 2

Value of $\displaystyle\int_{-1}^{1} \dfrac{x^5+|x|+1}{x^2+2|x|+1}\,dx$ is equal to :

2026: 22 May Shift 2

If $\int \frac{(\sqrt{x})^5}{(\sqrt{x})^7+x^6} dx = a\log\left|\frac{x^k}{1+x^k}\right| + C$ ; Where C is an arbitrary constant, then the value of $a.k$ is:

If ∫(1+xlog⁡x)xe−xdx=exf(x)+C\int \frac{(1 + x \log x)}{xe^{-x}} dx = e^x f(x) + C∫xe−x(1+xlogx)​dx=exf(x)+C, where C is constant of integration, then f(x)f(x)f(x) is

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

If $\int \frac{(1 + x \log x)}{xe^{-x}} dx = e^x f(x) + C$ , where C is constant of integration, then $f(x)$ is