AP EAMCET · Maths · Indefinite Integration
\(\int \frac{x^{e-1}+e^{x-1}}{x^e+e^x} d x=\)
- A \(\frac{-1}{e} \log \left|x^e+e^x\right|+\mathrm{C}\)
- B \(-e \log \left|x^{\mathrm{e}}+\mathrm{e}^x\right|+\mathrm{C}\)
- C \(\frac{1}{e} \log \left|x^e+e^x\right|+\mathrm{C}\)
- D \(e \log \left|x^{\mathrm{e}}+\mathrm{e}^x\right|+\mathrm{C}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{e} \log \left|x^e+e^x\right|+\mathrm{C}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \Rightarrow \quad\left(e x^{e-1}+e^x\right) d x=d t \\ & \Rightarrow \quad e\left(x^{e-1}+\frac{e^x}{e}\right) d x=d t \\ & \Rightarrow \quad e\left(x^{e-1}+e^{x-1}\right) d x=d t\end{aligned}\) Now, putting values from Eqs. (ii) and (iii) in Eq. ( \(i\) )…
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 a complex number \(z\) is such that \(\frac{z-2 i}{z-2}\) purely imaginary number and the locus of \(z\) is a closed curve, then the area of the region bounded by that closed curve and lying in the first quadrant isAP EAMCET 2024 Medium
- The locus of the point of intersection of the tangents at the
endpoints of normal chords of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) isAP EAMCET 2022 Hard - If \(\alpha, \beta, \gamma\) and \(\delta\) are zeroes of the polynomial equation \(x^4-3 x^2+6 x-12=0\), then the value of \(\frac{\alpha+\beta+\gamma}{\delta^2}+\frac{\alpha+\delta+\gamma}{\beta^2}\) \(+\frac{\alpha+\beta+\delta}{\gamma^2}+\frac{\delta+\beta+\gamma}{\alpha^2}\) is equal toAP EAMCET 2021 Easy
- A student writes an examination which contains eight true or false questions. If he answers six or more questions correctly, he passes the examination. If the student answers all the questions, then the probability that he fails in the examination isAP EAMCET 2024 Easy
- If the letters of the word "ASSASSINATION" are arranged at random in a row, then the probability that no two \(A^{\prime}\) 's come together is equal toAP EAMCET 2020 Easy
- The equation of the straight line perpendicular to \(5 x-2 y=7\) and passing through the point of intersection of the lines \(2 x+3 y=1\) and \(3 x+4 y=6\) isAP EAMCET 2005 Easy
More PYQs from AP EAMCET
- Given below are two statements:
Statement-I: For isothermal irreversible change of an ideal gas, \(q=-w=\mathrm{P}_{\text {ext }}\left(\mathrm{V}_{\text {final }}-\mathrm{V}_{\text {initial }}\right)\)
Statement - II: For adiabatic change, \(\Delta \mathrm{U}=\mathrm{W}_{\text {adiabatic }}\)
The correct answer isAP EAMCET 2024 Easy - A solid compound is formed by atoms of A (cations), B (cations) and O (anions). Atoms of O form hcp lattice. Atoms of A occupy 25\% of tetrahedral holes and atoms of B occupy \(50 \%\) octahedral holes. What is the molecular formula of solid?AP EAMCET 2024 Easy
- The lines represented by \(a x^2+2 h x y+b y^2=0\) are perpendicular to each other, if ........AP EAMCET 2020 Easy
- The area of the region that is common to the circle \(x^2+y^2=16 a^2\) and the parabola \(y^2=6 a x\) isAP EAMCET 2017 Easy
- If the lines \(k x+2 y-4=0\) and \(5 x-2 y-4=0\) are conjugate with respect to the circle \(x^2+y^2-2 x-2 y+1=0\), then \(k\) is equal toAP EAMCET 2016 Medium
- What is the volume (in \(\mathrm{mL}\) ) of \(20 \mathrm{vol} \mathrm{H}_2 \mathrm{O}_2\) required to completely react with \(500 \mathrm{~mL}\) of \(0.02 \mathrm{M}\) acidified \(\mathrm{KMnO}_4\) solution?AP EAMCET 2019 Medium