TS EAMCET · Maths · Indefinite Integration
If \(\frac{2 x+1}{(x-1)^2\left(x^2+1\right)}=\frac{A}{x-1}+\frac{B}{(x-1)^2}+\frac{C x+D}{x^2+1}\), then \(A+B+C+D=\)
- A 1
- B 2
- C \(\frac{3}{4}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
If \(\frac{2 x+1}{(x-1)^2\left(x^2+1\right)}=\frac{A}{x-1}+\frac{B}{(x-1)^2}+\frac{C x+D}{x^2+1}\) \(\Rightarrow \quad 2 x+1=A(x-1)\left(x^2+1\right)+B\left(x^2+1\right)\) \(+(C x+D)(x-1)^2\) \(\Rightarrow \quad 2 x+1=x^3(A+C)+x^2(-A+B-2 C+D)\) \(+x(A+C-2 D)+(-A+B+D)\) On…
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
- The length of the common chord of the circles \(x^2+y^2-6 x-4 y+9=0\) and \(x^2+y^2-8 x-6 y+23=0\) isTS EAMCET 2019 Easy
- If adj \(\left[\begin{array}{ccc}1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1\end{array}\right]=\left[\begin{array}{ccc}5 & m & -2 \\ 1 & 1 & 0 \\ -2 & -2 & n\end{array}\right]\), then \(m+n=\)TS EAMCET 2023 Medium
- The solution of \(\left(x^2+y^2\right) d x=2 x y d y\) is :TS EAMCET 2006 Easy
- Let x be a real number. Match the following:
TS EAMCET 2022 Easy - If \(\alpha+\beta=-2\) and \(\alpha^3+\beta^3=-56\), then the quadratic equation whose roots are \(\alpha\) and \(\beta\) isTS EAMCET 2008 Easy
- The equation of a circle which passes through the points of intersection of the circles \(2 x^2+2 y^2-2 x+6 y-3=0\), \(x^2+y^2+4 x+2 y+1=0\) and whose centre lies on the common chord of these circles isTS EAMCET 2024 Medium
More PYQs from TS EAMCET
- At \(300 \mathrm{~K}\), the osmotic pressure of a decinormal solution of sodium chloride is \(4.82 \mathrm{~atm}\). The degree of dissociation of sodium chloride is \(\mathrm{x} \times 10^{-2}\). The value of \(x\) is \(\left(\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{moi}^{-1}\right)\)TS EAMCET 2023 Medium
- X-rays of wavelength \(0.140 \mathrm{~nm}\) are scattered from a block of carbon. What will be the wavelengths of \(X\)-rays scattered at \(90^{\circ}\) ?TS EAMCET 2008 Medium
- Consider a frictionless ramp on which a smooth object is made to slide down from an initial height \(h\). The distance \(d\) necessary to stop the object on a flat track (of coefficient of friction \(\mu\) ), kept at the ramp end isTS EAMCET 2017 Medium
- Match the following items from List I into List II
Select the correct choiceTS EAMCET 2023 Medium - Which one of the following compounds forms a quaternary salt on reacting with excess methyl iodide?TS EAMCET 2004 Hard
- The magnitude of the force vector acting on a unit length of a thin wire carrying a current \(I=8 \mathrm{~A}\) at a point \(O\), if the wire is bent as shown in the figure with a radius, \(R=10 \pi \mathrm{cm}\) is
TS EAMCET 2019 Easy