CUET Mathematics - 1/x(x^5-1) dx is equal to | PYQs + Solutions

CUET Mathematics 2025 30 May Shift 2

Calculus

Medium

common

$\frac{1}{5}\log_e \left|\frac{x^5-1}{x^5}\right| + C$ ; C is an arbitrary constant

$\log_e \left|\frac{x^5-1}{x^5}\right| + C$ ; C is an arbitrary constant

$\frac{1}{5}(\log_e|x| + \log_e|x^5-1|) + C$ ; C is an arbitrary constant

$\log_e \left|\frac{x}{x^5-1}\right| + C$ ; C is an arbitrary constant

✅ Correct Option: 1

Related questions:

29 May Shift 2

Match List-I with List-II

List-I	List-II
Integral	Solution: C is an arbitrary constant
(A) $\int \frac{dx}{x^2 + 25}$	(I) $\frac{1}{10} \log \left\| \frac{5 + x}{5 - x} \right\| + C$
(B) $\int \frac{dx}{x^2 - 25}$	(II) $\log \|x + \sqrt{x^2 - 25}\| + C$
(C) $\int \frac{dx}{25 - x^2}$	(III) $\frac{1}{5} \tan^{-1} \left( \frac{x}{5} \right) + C$
(D) $\int \frac{dx}{\sqrt{x^2 - 25}}$	(IV) $\frac{1}{10} \log \left\| \frac{x - 5}{x + 5} \right\| + C$

Choose the correct answer from the options given below:

3 June Shift 1

$\int \sqrt{1 + \frac{x^2}{9}} dx$ is equal to

(Where C is an arbitrary constant)

26 May Shift 2

If $f(x)$ and $g(x)$ are continuous functions in [a, a] such that $f(x) = f(a - x)$ and $g(x) + g(a - x) = a$ then $\int_{0}^{a} f(x)g(x)dx =$

CUET Mathematics 2025 30 May Shift 2 PYQs