CUET · MATHS · PYQ PAPER 2025
For \(\ x \in R -\{-1,0,1\} \), \(\int \frac{1}{x-x^5} d x\) is equal to:
- A \(\frac{1}{4} \log _e\left|\frac{x^4}{1-x^4}\right|+c\) : where \(c\) is constant of integration.
- B \(-\frac{1}{4} \log _e\left|\frac{x^4}{1-x^4}\right|+c\) : where \(c\) is constant of integration.
- C \(4 \log _e\left|\frac{x^4}{1-x^4}\right|+c\) : where \(c\) is constant of integration.
- D \(-4 \log _e\left|\frac{x^4}{1-x^4}\right|+c\) : where \(c\) is constant of integration.
Answer & Solution
Correct Answer
(A) \(\frac{1}{4} \log _e\left|\frac{x^4}{1-x^4}\right|+c\) : where \(c\) is constant of integration.
Step-by-step Solution
Detailed explanation
\(\int \frac{1}{x-x^5} d x = \int \left( \frac{1}{x} + \frac{x^3}{1-x^4} \right) d x\) \(= \ln|x| - \frac{1}{4} \ln|1-x^4| + c\) \(= \frac{1}{4} (4 \ln|x| - \ln|1-x^4|) + c\) \(= \frac{1}{4} \log _e\left|\frac{x^4}{1-x^4}\right|+c\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from MATHS
- Rolle's theorem holds for the function \(x^3+b x^2+c x, 1 \leq x \leq 2\) at the point \(\frac{4}{3}\), the respective values of \(b\) and \(c\) are :CUET 2023 Easy
- If a random variable \(X\) has the following probability distribution :
then,X 0 1 2 3 P(X) K \(\frac{K}{2}\) \(\frac{K}{4}\) \(\frac{K}{8}\)
Match List-I with List-II
Choose the correct answer from the options given below :List-I List-II (A) The value of \(K\) is (I) \(2 / 15\) (B) \(P(0<X<2)\) is (II) \(1 / 15\) (C) \(P(1<X<3)\) is (III) \(8 / 15\) (D) \(P(X>2)\) is (IV) \(4 / 15\) CUET 2025 Hard - If \(\left|\begin{array}{ll}2 & 4 \\ 5 & 1\end{array}\right|=\left|\begin{array}{cc}2 x & 4 \\ 6 & x\end{array}\right|\), then \(x\) is equal to:CUET 2023 Easy
- Which of the following is true?CUET 2023 Easy
- The integrating factor of the differential equation \(\frac{d y}{d x}+y \cot x=2 x+x^2 \cot x, x \neq 0\) isCUET 2023 Medium
- The integrating factor of the differential equation \(\frac{d y}{d x}=x+x y\) is:CUET 2025 Medium
More PYQs from CUET
- n-Hexane is obtained when glucose isCUET 2025 Medium
- Match List-I with List-II
Choose the correct answer from the options given below:List-I (Types of evolution) List-II (Examples) (A) Divergent evolution (I) Moths (B) Adaptive radiation (II) Eyes of octopus and mammals (C) Convergent evolution (III) Darwin's finches (D) Industrial melanism (IV) Thorn of Bougainvillea and tendrils of Cucurbita CUET 2025 Hard - Read the following passage carefully and answer the given questions
The separated DNA fragments can be visualized only after staining the DNA with ethidium bromide followed by exposure to UV radiation. Bright orange colored bands of DNA in ethidium bromide stained gel exposed to UV light can be seen. The separated bands of DNA are cut out from the agarose gel and extracted from the gel piece. This step is known as elution. The DNA fragments purified in this way are used in constructing recombinant DNA by joining them with a cloning vector.
The DNA band appears orange due to -CUET 2025 Easy - If A is a square matrix of order 3 and \(|A| = -2\) then, \(|-2A^{-1}|\) is:CUET 2023 Medium
- Let A be any skew-symmetric matrix (where \(A^T\) is Transpose of matrix A ), then which of the following statements are correct?
(A) \(A^2\) is a symmetric matrix
(B) \(A^2\) is a skew-symmetric matrix
(C) \(A^T A=-A^2\)
(D) \(A^T A-A A^T=O\)
Choose the correct answer from the options given below :CUET 2025 Medium - Given equation of the plane is \(5x + 2y - 3z = 17\). Then,
A. A point \((2, 2, -1)\) lies on the plane
B. The direction cosines of normal to plane are \((2, 2, -1)\)
C. Coordinates of foot of perpendicular from origin are \((5, 2, -3)\)
D. The plane does not pass through the origin
Choose the correct answer from the options given below:CUET 2023 Medium