COMEDK · Maths · 28. Indefinite Integration
\(\int \dfrac{x}{(x-1)(x-2)^2} d x=a \log \left|\dfrac{x-1}{x-2}\right|+\dfrac{b}{(x-2)}+c\) then
- A \(a=1, b=2\)
- B \(a=-1, b=2\)
- C \(a=1, b=-2\)
- D \(a=-1, b=-2\)
Answer & Solution
Correct Answer
(C) \(a=1, b=-2\)
Step-by-step Solution
Detailed explanation
Let the integrand be \(\dfrac{x}{(x-1)(x-2)^2} = \dfrac{A}{x-1} + \dfrac{B}{x-2} + \dfrac{C}{(x-2)^2}\). Multiplying by \((x-1)(x-2)^2\), we get \(x = A(x-2)^2 + B(x-1)(x-2) + C(x-1)\). Setting \(x=1\), we get \(1 = A(1-2)^2\), so \(A=1\). Setting \(x=2\), we get \(2 = C(2-1)\),…
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 total number of terms in \((x-y)^{20}+(x+y)^{20}\) isCOMEDK 2024 Easy
- 6 boys and 6 girls in a row at random. The probability that all the girls sit together isCOMEDK 2015 Easy
- The vector equation of two lines are
\(\begin{aligned}
& \vec{r}=(1-t) \hat{\imath}+(t-2) \hat{\jmath}+(3-2 t) \hat{k} \\
& \vec{r}=(s+1) \hat{\imath}+(2 s-1) \hat{\jmath}-(2 s+1) \hat{k}
\end{aligned}\)
Then the shortest distance between them isCOMEDK 2024 Medium - The length of the latus rectum of a conic \(49 y^2-16 x^2=784\) isCOMEDK 2025 Easy
- The line \(\dfrac{x-2}{3}=\dfrac{y-3}{4}=\dfrac{z-4}{5}\) is parallel to the planeCOMEDK 2021 Easy
- If \(A=\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]\), then \(A^{n}\) isCOMEDK 2018 Easy
More PYQs from COMEDK
- If \(A=\left|\begin{array}{lll}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{array}\right|\) and \(B=\left|\begin{array}{ccc}c_{1} & c_{2} & c_{3} \\ a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3}\end{array}\right|\) thenCOMEDK 2019 Medium
- If \(\tan x^{\circ} \tan 2^{\circ} \tan 3^{\circ} \ldots \ldots \ldots \ldots . \tan 88^{\circ} \tan y^{\circ}=1\) then \(\cot (x+y)=\)COMEDK 2025 Medium
- A given volume of gas at NTP is allowed to expand 6 times of its original volume, first under isothermal condition and then under adiabatic condition. Which of the given statement is correct?
[Given \(\dfrac{C_p}{C_v}=\gamma=1.4\) ]COMEDK 2025 Medium - When 2-bromopentane is heated with alcoholic solution of potassium hydroxide, the major product obtained isCOMEDK 2014 Easy
- In a single slit diffraction experiment, for slit width '\(\alpha\)' the width of the central maxima is '\(\beta\)'. If we double the slit width then the corresponding width of the central maxima will be:COMEDK 2024 Easy
- An important reaction of acetone is auto-condensation in presence of concentrated sulphuric acid to give the aromatic compoundCOMEDK 2013 Hard