Question:
If $\frac{x^{3}}{\left(2x-1\right)\left(x-1\right)^{2}} = A + \frac{B}{2x-1}+ \frac{C}{x-1}+ \frac{D}{\left(x-1\right)^{2}} $, then $2A - 3B + 4C + 5D = $
If $\frac{x^{3}}{\left(2x-1\right)\left(x-1\right)^{2}} = A + \frac{B}{2x-1}+ \frac{C}{x-1}+ \frac{D}{\left(x-1\right)^{2}} $, then $2A - 3B + 4C + 5D = $
Updated On: Apr 4, 2024
- $\frac{21}{2}$
- $\frac{23}{2}$
- $\frac{17}{2}$
- $\frac{19}{2}$
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Answer (c) $\frac{17}{2}$
Was this answer helpful?
0
0
Top Questions on Integration by Partial Fractions
- Let {an}n=0∞ be a sequence such that a0=a1=0 and an+2=3an+1−2an+1,∀ n≥0. Then a25a23−2a25a22−2a23a24+4a22a24 is equal to
- JEE Main - 2025
- Mathematics
- Integration by Partial Fractions
- Find the value of \( \frac{5}{6} + \frac{3}{4} \).
- MHT CET - 2025
- Mathematics
- Integration by Partial Fractions
- Let for \( f(x) = 7\tan^8 x + 7\tan^6 x - 3\tan^4 x - 3\tan^2 x \), \( I_1 = \int_0^{\frac{\pi}{4}} f(x)dx \) and \( I_2 = \int_0^{\frac{\pi}{4}} x f(x)dx \). Then \( 7I_1 + 12I_2 \) is equal to:
- JEE Main - 2025
- Mathematics
- Integration by Partial Fractions
- If ∫ (2x + 3)/((x - 1)(x^2 + 1)) dx = log_x {(x - 1)^(5/2)(x^2 + 1)^a} - (1/2) tan^(-1)x + C, then the value of a is:
- MHT CET - 2025
- Mathematics
- Integration by Partial Fractions
- Find the value of the integral: ∫ (2x + 3)/((xy)(x^2 + 1)) dx
- MHT CET - 2025
- Mathematics
- Integration by Partial Fractions
View More Questions
Questions Asked in AP EAMCET exam
- At 300 K, 6 g of urea was dissolved in 500 mL of water. What is the osmotic pressure (in atm) of the resultant solution? (R = 0.082 L atm K$^{-1}$ mol$^{-1}$) (C=12;N=14;O=16;H=1)
- AP EAMCET - 2024
- Colligative Properties
- The gravitational potential energy of a body on the surface of the Earth is \(E\). If the body is taken from the surface of the Earth to a height equal to \(150%\) of the radius of the Earth, its gravitational potential energy is:
- AP EAMCET - 2024
- Gravitational Potential Energy
The mass of particle X is four times the mass of particle Y. The velocity of particle Y is four times the velocity of X. The ratio of de Broglie wavelengths of X and Y is:
- AP EAMCET - 2024
- Molecular Polarity
- The focal length of a thin converging lens in air is 20 cm. When the lens is immersed in a liquid, it behaves like a concave lens of power 1 D. If the refractive index of the material of the lens is 1.5, the refractive index of the liquid is
- AP EAMCET - 2024
- Wave optics
- A line \( L \) passing through the point \( P(-5,-4) \) cuts the lines \( x - y - 5 = 0 \) and \( x + 3y + 2 = 0 \) respectively at \( Q \) and \( R \) such that \[ \frac{18}{PQ} + \frac{15}{PR} = 2, \] then the slope of the line \( L \) is:
- AP EAMCET - 2024
- Coordinate Geometry
View More Questions
Concepts Used:
Integration by Partial Fractions
The number of formulas used to decompose the given improper rational functions is given below. By using the given expressions, we can quickly write the integrand as a sum of proper rational functions.
For examples,
