CUET · MATHS · PYQ PAPER 2023
The value of the integral \(\int e^x\left(\frac{1}{x}-\frac{1}{x^2}\right) d x\) is:
- A \(\frac{e^x}{x}+C\), where C is a constant
- B \(\frac{e^{-x}}{x}+C\), where C is a constant
- C \(e^x+C\), where C is a constant
- D \(e^{-x}+C\), where C is a constant
Answer & Solution
Correct Answer
(A) \(\frac{e^x}{x}+C\), where C is a constant
Step-by-step Solution
Detailed explanation
We use \(\int e^x(f(x)+f'(x))dx = e^x f(x) + C\), where \(f(x)=\frac{1}{x}\) and \(f'(x)=-\frac{1}{x^2}\). \(\int e^x\left(\frac{1}{x}-\frac{1}{x^2}\right) d x = e^x\left(\frac{1}{x}\right)+C\) \(= \frac{e^x}{x}+C\)
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
- The interval in which the function given by \(f(x) = \sin^4 x + \cos^4 x\), x \(\in\) [0, \(\frac{\pi}{2}\)] is decreasing is:CUET 2023 Easy
- If \(2 P(A)=P(B)=\frac{5}{13}\) and \(P(A \mid B)=\frac{2}{5}\), then \(P(A \cap B)\) isCUET 2025 Easy
- The minimum value of \(a x+b y\), where \(x y=c^2\) and \(a, b, c\) are positive, is:CUET 2023 Easy
- Which of the following are correct?
(A) Time series analysis does not help to understand the behavior of a variable in the past.
(B) Time series predict the future behavior of variable.
(C) Time series helps to plan future operations.
(D) The main aim of the time series analysis is to derive conclusions after arranging the time series in a systematic manner.
Choose the correct answer from the options given below:CUET 2025 Medium - If \(A\) is a square matrix of order 3 and \(|A|=5\), then \([\operatorname{Adj} A] A\) is____________.CUET 2023 Hard
- If \(y=\left\{\log \left(x+\sqrt{x^2+1}\right)\right\}^2\) then \(\left(1+x^2\right) \frac{d^2 y}{d x^2}+x \frac{d y}{d x}=\)CUET 2023 Medium
More PYQs from CUET
- Choose the correct statements from the following related to glycine amino acid.
(A). Water soluble \(\alpha\)-amino acid.
(B). It has both amino and carboxylic groups in its structure.
(C). It is optically inactive.
(D). It is a non-essential amino acid.
Choose the correct answer from the options given below :CUET 2023 Hard - A transmitting antenna at the top of a tower has a height 32 m and the height of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in LOS mode? Given radius of earth \(= 6.4 \times 10^6\) m.CUET 2023 Hard
- When light of suitable frequency is incident on a photosensitive material, photo electrons are ejected and photoelectric current flows. If the intensity of the incident light is increased, thenCUET 2025 Hard
- The pollination which involves the transfer of pollen grain from the anther
to the stigma of another flower of the same plant is known as-CUET 2025 Easy - Match List - I with List - II.
List - I List - II (A) Streptokinase (I) immuno suppressive agent (B) Cyclosporin A (II) clot buster (C) Statin (III) helpful in removing oil stains (D) Lipase (IV) blood cholesterol lowering agents CUET 2023 Hard - Which of the following step is not the part of downstream processing?CUET 2025 Medium