CUET · MATHS · PYQ PAPER 2025
\(\int \frac{x}{(x-1)(x-2)} d x\) is equal to (where C is a constant of integration)
- A \(\log _e\left|\frac{(x-1)^2}{x-2}\right|+C\)
- B \(\log _e\left|\frac{(x-2)^2}{x-1}\right|+C\)
- C \(\log _e\left|(x-2)(x-1)^2\right|+C\)
- D \(\log _e\left|\frac{x-1}{(x-2)^2}\right|+C\)
Answer & Solution
Correct Answer
(B) \(\log _e\left|\frac{(x-2)^2}{x-1}\right|+C\)
Step-by-step Solution
Detailed explanation
\(\frac{x}{(x-1)(x-2)} = \frac{-1}{x-1} + \frac{2}{x-2}\) \(\int \left( \frac{-1}{x-1} + \frac{2}{x-2} \right) dx = -\log _e |x-1| + 2\log _e |x-2| + C\) \(= \log _e \left| \frac{(x-2)^2}{x-1} \right| + C\)
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
- If \(\int \frac{d x}{(x-1)^{3 / 4}(x+2)^{5 / 4}}=\alpha[1-g(x)]^\beta+c\), where \(c\) is a constant of integration, then which of the
following are true?
(A) \(\alpha=\frac{2}{3}\)
(B) \(\beta=\frac{3}{4}\)
(C) \(3 \alpha+4 \beta=5\)
(D) \(g(x)=\frac{3}{x+2}\)
Choose the correct answer from the options given below:CUET 2025 Hard - If A and B are two events such that \(P(A) \neq 0\) and \(P(A / B)=1\) then :CUET 2023 Hard
- In a Binomial distribution, the probability of getting a success is \(\frac{3}{4}\) and the variance is \(\frac{3}{8}\) then the probability of no success is:CUET 2025 Medium
- Let \(f(x)=x^3-6 x^2+9 x-8\) be a function, then which of the following statements are TRUE?
(A) \(f^{\prime}(x)=3(x-1)(x-3)\)
(B) The critical points of the function are \(x=1\) and \(x=3\)
(C) \(x=1\) is the point of local minimum
(D) The local maximum value is -4
Choose the correct answer from the options below :CUET 2025 Easy - Cosine of the acute angle between the lines \(\frac{x-3}{2}=\frac{y-2}{1}=\frac{x-5}{2}\) and \(\frac{x-1}{6}=\frac{y-3}{-3}=\frac{z+6}{2}\) isCUET 2025 Hard
- \(\left|\begin{array}{lll}1 & 2 & 3 \\4 & 5 & 6 \\7 & 8 & 9\end{array}\right|=x\left|\begin{array}{ll}2 & 3 \\8 & 9\end{array}\right|+y\left|\begin{array}{ll}1 & 3 \\7 & 9\end{array}\right|+z\left|\begin{array}{ll}1 & 2 \\7 & 8\end{array}\right|\)
Then \(x+y+z\) is:CUET 2023 Medium
More PYQs from CUET
- Which of the following reagents are used for denaturation of alcoholCUET 2023 Easy
- Which of the following statements is not correct for electromagnetic induction?CUET 2025 Medium
- Select the correct statement.CUET 2025 Easy
- The value of the integral \(I=\int_{-1}^2|x| d x\) is :CUET 2023 Hard
- Presence of nitrate ions can be detected by adding freshly prepared \(\text{FeSO}_4\) solution. Then concentrated \(\text{H}_2\text{SO}_4\) is added along the walls of the test tube.
A brown ring is formed at the interface having the formula \([\text{Fe(H}_2\text{O)}_5\text{(NO)}]^{2+}\.
The oxidation state of Fe in this complex isCUET 2023 Easy - Match List-l with List-ll:
Choose the correct answer from the options given below:List-l (Items) List-ll (Properties) (A) Primary batteries (I) Pollution free energy converter. (B) Secondary batteries (II) Takes place in the presence of air, moisture and H+ (C) Fuel cells (III)Large number of charging/discharging and long-lasting (D) Corrosion (IV) Mercury cell is used in hearing aids CUET 2025 Easy