TS EAMCET · Maths · Indefinite Integration
\(\int \frac{x+1}{x\left(1+x e^x\right)} d x=\)
- A \(\log \left|\frac{1+x e^x}{x+1}\right|+C\)
- B \(\log \left|\frac{x e^x}{1+x e^x}\right|+C\)
- C \(\log \left|\frac{(x+1) e^x}{1+e^x}\right|+C\)
- D \(\log \left|\frac{x e^x}{x+e^x}\right|+C\)
Answer & Solution
Correct Answer
(B) \(\log \left|\frac{x e^x}{1+x e^x}\right|+C\)
Step-by-step Solution
Detailed explanation
Let \[ I=\int \frac{x+1}{x\left(1+x e^x\right)} d x \] \(\operatorname{Put}\left(1+x e^x\right)=t \Rightarrow(x+1) e^x d x=d t\)…
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
- At any point on a curve, the slope of the tangent is equal to the sum of abscissa and the product of ordinate and abscissa of that point. If the curve passes through , then the equation of the curve isTS EAMCET 2018 Medium
- Suppose \(X\) follows a binomial distribution with parameters \(n\) and \(p\), where \(0 < p < 1\). If \(\frac{P(X=r)}{P(X=n-r)}\) is independent of \(n\) for every \(r\), then \(p\) is equal toTS EAMCET 2012 Medium
- If \(\sin \mathrm{h} x=\frac{-1}{2}\) then \(\tan \mathrm{h} 2 x=\)TS EAMCET 2022 Easy
- Let \(A\) and \(B\) be not mutually exclusive events. If \(P(A)=\frac{4}{9}, P(A \cap \bar{B})=\frac{3}{7}\) then \(P\left(\frac{B}{A}\right)=\)TS EAMCET 2020 Easy
- If \(\frac{3 x+2}{(x+1)\left(2 x^2+3\right)}=\frac{A}{x+1}+\frac{B x+C}{2 x^2+3}\), then \(A-B+C=\)TS EAMCET 2018 Easy
- The system of equations \(x+3 y+7=0\), \(3 x+10 y-3 z+18=0\) and \(3 y-9 z+2=0\) hasTS EAMCET 2024 Medium
More PYQs from TS EAMCET
- The main products formed when copper metal is reacted with concentrated areTS EAMCET 2021 Easy
- Mustard gas among the following isTS EAMCET 2021 Medium
- If the kinetic energy in \(\mathrm{J}\), of \(\mathrm{CH}_4\) (molar mass \(=16 \mathrm{~g} \mathrm{~mol}^{-1}\) ) at \(T(\mathrm{~K})\) is \(X\), the kinetic energy in \(\mathrm{J}\), of \(\mathrm{O}_2\) (molar mass \(=32 \mathrm{~g} \mathrm{~mol}^{-1}\) ) at the same temperature isTS EAMCET 2016 Easy
- In a triangle, if the length of the sides and are three consecutive natural numbers and thenTS EAMCET 2021 Easy
- A source and an observer move away from each other with same velocity of \(10 \mathrm{~ms}^{-1}\) with respect to ground. If the observer finds the frequency of sound coming from the source as \(1980 \mathrm{~Hz}\), then actual frequency of the source is (speed of sound in air \(=340 \mathrm{~ms}^{-1}\) )TS EAMCET 2023 Medium
- A particle starts from origin at time \(t=0\) and moves in positive \(x\)-direction. Its velocity \(\mathbf{v}\) varies with times as \(\mathbf{v}=10 \hat{t} \mathrm{~cm} / \mathrm{s}\). The distance covered by the particle in \(8 \mathrm{~s}\) will beTS EAMCET 2018 Easy