MHT CET · Maths · Indefinite Integration
\(\int e^{x} \frac{(x-1)}{x^{2}} d x\) is equal to
- A \(\frac{e^{x}}{x^{2}}+c\)
- B \(\frac{-e^{x}}{x^{2}}+c\)
- C \(\frac{e^{x}}{x}+c\)
- D \(\frac{-e^{x}}{x}+c\)
Answer & Solution
Correct Answer
(C) \(\frac{e^{x}}{x}+c\)
Step-by-step Solution
Detailed explanation
\(\int e^{x}\left(\frac{x-1}{x^{2}}\right) d x\)
\(\quad=\int e^{x}\left(\frac{1}{x}-\frac{1}{x^{2}}\right) d x\)
\(=\frac{e^{x}}{x}+c\left[\because \int e^{x}\left[f(x)+f^{\prime}(x)\right] d x=e^{x} f(x)+c\right]\)
\(\quad=\int e^{x}\left(\frac{1}{x}-\frac{1}{x^{2}}\right) d x\)
\(=\frac{e^{x}}{x}+c\left[\because \int e^{x}\left[f(x)+f^{\prime}(x)\right] d x=e^{x} f(x)+c\right]\)
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 \(\mathrm{x}=\mathrm{e}^{\mathrm{t}}(\sin \mathrm{t}-\cos \mathrm{t})\) and \(\mathrm{y}=\mathrm{e}^{\mathrm{t}}(\sin \mathrm{t}+\cos \mathrm{t})\), then \(\frac{\mathrm{dy}}{\mathrm{dx}}\) at \(\mathrm{t}=\frac{\pi}{3}\) isMHT CET 2021 Medium
- The least distance of the point \(A(10,7)\) from the circle \(x^2+\mathrm{y}^2-4 x-2 \mathrm{y}-20=0\) is length of seg. AM . If \(\mathrm{MM}^{\prime}\) is the diameter of the circle, then the lengths of AM and \(\mathrm{AM}^{\prime}\) are respectively _______ , ______ unitsMHT CET 2025 Medium
- If \(n(A)=4, n(B)=2\). Then the number of subsets of the set \(\mathrm{A} \times \mathrm{B}\) each having at least 3 elements areMHT CET 2024 Easy
- Let \(P(3,2,6)\) be a point in space and \(Q\) be a point on the line \(\bar{r}=\hat{i}-\hat{j}+2 \hat{k}+\mu(-3 \hat{i}+\hat{j}+5 \hat{k})\). Then the value of \(\mu\) for which the vector \(\overline{\mathrm{PQ}}\) is parallel to the plane \(x-4 y+3 z=1\) isMHT CET 2024 Hard
- The Cartesian equation of the lien passing through the points \(\mathrm{A}\) \((2,2,1)\) and \(B(1,3,0)\) isMHT CET 2021 Easy
- \(\int \frac{x^3-7 x+6}{x^2+3 x} \mathrm{~d} x=\)MHT CET 2024 Hard
More PYQs from MHT CET
- Let the speed of light and the polarising angle for a given medium be ' \(V\) ' and ' \(\mathrm{i}_p\) ' respectively. The relation between them is ( \(C=\) speed of light in vacuum)MHT CET 2025 Medium
- if \(\bar{a}, \overline{\mathrm{~b}}, \overline{\mathrm{c}}\) are non coplanar unit vectors such that \(\bar{a} \times(\overline{\mathrm{b}} \times \overline{\mathrm{c}})=\frac{\overline{\mathrm{b}}+\overline{\mathrm{c}}}{\sqrt{2}}\) Then the angle between \(\bar{a}\) and \(\overline{\mathrm{b}}\) isMHT CET 2025 Medium
- The equation of the lines passing through the origin and having slopes 3 and \(-\frac{1}{3}\), isMHT CET 2010 Easy
- The pH of a sample of vinegar is 3.76. Calculate the concentration of hydrogen ion in it in \(\mathrm{mol~} \mathrm{dm}^{-3}\) ?MHT CET 2025 Easy
- Consider a soap film on a rectangular frame of wire of area \(3 \times 3 \mathrm{~cm}^2\). If the area of the soap film is increased to \(5 \times 5 \mathrm{~cm}^2\), the work done in the process will be (surface tension of soap solution is \(2.5 \times 10^{-2} \mathrm{~N} / \mathrm{m}\) )MHT CET 2023 Medium
- A body of mass ' \(\mathrm{m}\) ' is moving with speed ' \(\mathrm{V}\) ' along a circular path of radius ' \(r\) '. Now the speed is reduced to \(\frac{\mathrm{V}}{2}\) and radius is increased to ' \(3 r\) '. For this change, initial centripetal force needs to beMHT CET 2021 Medium