TS EAMCET · Maths · Indefinite Integration
\(\int \frac{3 x+2}{4 x^2+4 x+5} d x=\mathrm{A} \log \left(4 x^2+4 x+5\right)+\mathrm{BTan}^{-1}\left(\frac{2 x+1}{2}\right)+\mathrm{c}\), then \(\mathrm{A}+\mathrm{B}=\)
- A \(\frac{1}{2}\)
- B \(\frac{3}{4}\)
- C \(\frac{3}{8}\)
- D \(\frac{1}{8}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Let \( 3x+2 = K_1(8x+4) + K_2 \) \( 8K_1 = 3 \implies K_1 = \frac{3}{8} \) \( 4K_1 + K_2 = 2 \implies 4\left(\frac{3}{8}\right) + K_2 = 2 \implies \frac{3}{2} + K_2 = 2 \implies K_2 = \frac{1}{2} \)…
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
- Let \(\alpha, \beta, \gamma\) be real numbers. If
\(\left(\begin{array}{ccc}7 & 5 & \alpha \\ \beta & 2 & 11 \\ 3 & \gamma & 1\end{array}\right)\left(\begin{array}{l}1 \\ 3 \\ 2\end{array}\right)=\left(\begin{array}{c}\alpha+\beta \\ -2 \alpha+\beta-2 \gamma \\ \alpha+2 \beta+3 \gamma\end{array}\right)\) then \(100+\frac{2 \alpha+11 \beta}{\gamma}=\)TS EAMCET 2022 Medium - The set of all points that forms a triangle of area 15 sq units with the points \((1,-2)\) and \((-5,3)\) lies onTS EAMCET 2019 Easy
- The solution of \(\frac{d y}{d x}+1=e^{x+y}\) isTS EAMCET 2007 Medium
- If \(1, \omega, \omega^2\) are the cube roots of unity and \(1, \alpha, \alpha^2, \alpha^3\) are the fourth roots of unity in usual notation then \(\alpha+\alpha \omega-\alpha^3 \omega^2=\)TS EAMCET 2022 Hard
- If the perpendicular distance from the focus of an ellipse \(\frac{x^2}{9}+\frac{y^2}{b^2}=1(b < 3)\) to its corresponding directrix is \(\frac{4}{\sqrt{5}}\), then the slope of the tangent to this ellipse drawn at \(\left(\frac{3}{\sqrt{2}}, \frac{b}{\sqrt{2}}\right)\) isTS EAMCET 2025 Medium
- The value that should be assigned to \(f(0)\) so that the function \(f(x)=(x+1)^{\cot x}\) is continuous at \(x=0\), isTS EAMCET 2015 Easy
More PYQs from TS EAMCET
- The angle between the line joining the points \((1,-2),(3,2)\) and the line \(x+2 y-7=0\) isTS EAMCET 2018 Medium
- Which one of the following statements is correct?TS EAMCET 2018 Easy
- Let \(\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) and \(\mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\). If \(\mathbf{c}\) is \(\mathbf{a}\) unit vector such that \(\left[\begin{array}{lll}\mathbf{a} & \mathbf{b} & \mathbf{c}\end{array}\right]\) is maximum, then \(\mathbf{c}=\)TS EAMCET 2020 Easy
- What is the major product Z in the given reaction sequence?
\(\left(\mathrm{CH}_3\right)_2 \mathrm{C}=\mathrm{O} \xrightarrow[\text { (2) } \mathrm{H}_3 \mathrm{O}^{+}]{(\mathrm{l}) \mathrm{C}_2 \mathrm{H}_3 \mathrm{MgBr}^{+}} \mathrm{X}\) i) \(\mathrm{SOCl}_2 \xrightarrow[\Delta]{\text { ii) } \mathrm{CH}_3 \mathrm{ONa}} Y \xrightarrow[\text { Peroxide }]{\mathrm{HBr}} Z\)TS EAMCET 2024 Hard - Uranium has two isotopes of masses 235 and 238 wits. If both of them are present in wranium hexafluoride gas, find the percentage ratio of difference in rms velocities of two isotopes to the rms velocity of heavier isotope.TS EAMCET 2016 Easy
- A hollow cylinder and a solid cylinder initially at rest at the top of an inclined plane are rolling down without slipping. If the time taken by the hollow cylinder to reach the bottom of the inclined plane is 2 s , the time taken by the solid cylinder to reach the bottom of the inclined plane isTS EAMCET 2024 Medium