AP EAMCET · Maths · Indefinite Integration
\(\int e^x\left(\log x+\frac{1}{x^2}\right) d x=\)
- A \(e^x\left(\log x+\frac{1}{x}\right)+C\)
- B \(\mathrm{e}^{\mathrm{x}}\left(\log \mathrm{x}-\frac{1}{\mathrm{x}}\right)+\mathrm{C}\)
- C \(e^x\left(\log x+\frac{2}{x}\right)+C\)
- D \(\mathrm{e}^{\mathrm{x}}\left(\log \mathrm{x}-\frac{2}{\mathrm{x}}\right)+\mathrm{C}\)
Answer & Solution
Correct Answer
(B) \(\mathrm{e}^{\mathrm{x}}\left(\log \mathrm{x}-\frac{1}{\mathrm{x}}\right)+\mathrm{C}\)
Step-by-step Solution
Detailed explanation
\(\int e^x\left(\log x+\frac{1}{x^2}\right) d x\) \(\begin{aligned} & =\int e^x\left(\log x-\frac{1}{x}+\frac{1}{x}+\frac{1}{x^2}\right) d x \\ & =e^x\left(\log x-\frac{1}{x}\right)+C\end{aligned}\)
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 \(\mathrm{M}_1\) and \(\mathrm{M}_2\) are the maximum values of \(\frac{1}{11 \cos 2 x+60 \sin 2 x+69}\) and \(3 \cos ^2 5 x+4 \sin ^2 5 x\) respectively, then \(\frac{M_1}{M_2}=\)AP EAMCET 2024 Medium
- Angle between the planes \(\vec{r} \cdot(2 \hat{i}+4 \hat{j}-3 \hat{k})=5\) and \(\vec{r} \cdot(5 \hat{i}+3 \hat{j}+4 \hat{k})=7\) isAP EAMCET 2024 Easy
- The sum of all the real roots of the equation isAP EAMCET 2022 Medium
- The function \(f(x)=\frac{e^{|x|}-e^{-x}}{e^x+e^{-x}}+\cos ^3\left(\frac{x}{2}\right)\) from \(R\) to itself isAP EAMCET 2020 Medium
- If \(\tan \mathrm{h}^{-1}(x+i y)=\frac{1}{2} \tan \mathrm{h}^{-1}\left(\frac{2 x}{1+x^2+y^2}\right)+\frac{i}{2} \tan ^{-1}\left(\frac{2 y}{1-x^2-y^2}\right)\), where \(x, y \in \mathbf{R}\), then \(\tan \mathrm{h}^{-1}(i y)=\)AP EAMCET 2020 Hard
- The interval in which the function \(f(x)=\frac{\log (7+x)}{\log (3+x)}(x>0)\) decreases isAP EAMCET 2019 Easy
More PYQs from AP EAMCET
- What is the remainder of \(2 x^3-5 x^2+7\) when divided with \((x-2)\) ?AP EAMCET 2020 Easy
- Find \(\alpha^4+\beta^4\) if \(\alpha, \beta\) are the roots of equation \(x^2+x+1=0\).AP EAMCET 2020 Easy
- In the given pressure \((\mathrm{P})\) - absolute temperature \((\mathrm{T})\) graph of an ideal gas, the relation between volumes \(V_1, V_2, V_3\) and \(\mathrm{V}_4\) is
AP EAMCET 2023 Easy - The correctly matched set of the following isAP EAMCET 2024 Medium
- Which of the following is a linear molecule?AP EAMCET 2005 Easy
- In \(\triangle A B C\), if \(a: b: c=4: 5: 6\), then the ratio between the circumradius and the inradius isAP EAMCET 2021 Medium