Download App

STD 12 - 7.1 inderfinite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.1 inderfinite integral4 Marks
MCQ
Correct evaluation of $\int_{}^{} {\frac{x}{{(x - 2)(x - 1)}}\;dx} $ is

(where $p$  is an arbitrary constant)

  • ✓
    ${\log _e}\frac{{{{(x - 2)}^2}}}{{(x - 1)}} + p$
  • B
    ${\log _e}\frac{{(x - 1)}}{{(x - 2)}} + p$
  • C
    $\frac{{x - 1}}{{x - 2}} + p$
  • D
    $2{\log _e}\left( {\frac{{x - 2}}{{x - 1}}} \right) + p$
✓

Answer

Correct option: A.
${\log _e}\frac{{{{(x - 2)}^2}}}{{(x - 1)}} + p$
a
(a)$\int_{}^{} {\frac{x}{{(x - 2)(x - 1)}}\,dx} = - \int_{}^{} {\frac{1}{{x - 1}}\,dx + \int_{}^{} {\frac{2}{{x - 2}}\,dx} } $
$ = - {\log _e}(x - 1) + 2{\log _e}(x - 2) + c = {\log _e}\frac{{{{(x - 2)}^2}}}{{(x - 1)}} + p.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A card is drawn from a well shuffled pack of cards. The probability of getting a queen of club or king of heart is
→
Let $|\vec{a}|=2,|\vec{b}|=3$ and the angle between the vectors $\vec{a}$ and $\vec{b}$ be $\frac{\pi}{4}$. Then $|(\vec{a}+2 \vec{b}) \times(2 \vec{a}-3 \vec{b})|^2$ is equal to
→
If $y = \sqrt {{{(x - a)(x - b)} \over {(x - c)(x - d)}}} $, then ${{dy} \over {dx}} = $
→
If $\quad A=\left[\begin{array}{cc}\cos \theta & \text { isin } \theta \\ \operatorname{isin} \theta & \cos \theta\end{array}\right], \left(\theta=\frac{\pi}{24}\right)$ and $A^{5}=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right],$ where $i=\sqrt{-1},$ then which one of the following is not true?
→
The ratio in which $x$-axis divides the join of the points $(2, -3)$ and $(5, 6)$ is
→
If $x $ and  $y $ are two unit vectors and $\pi $ is the angle between them, then $\frac{1}{2}|x-y|$  is equal to
→
If ${\cos ^{ - 1}}\sqrt p + {\cos ^{ - 1}}\sqrt {1 - p} + {\cos ^{ - 1}}\sqrt {1 - q} = \frac{{3\pi }}{4},$ then the value of  $q $ is
→
The number of ways of giving $20$ distinct oranges to $3$ children such that each child gets atleast one orange is $............$.
→
If $\alpha ,\;\beta ,\;\gamma $ are the geometric means between $ca,\;ab;\;ab,\;bc;\;bc,\;ca$ respectively where $a,\;b,\;c$ are in A.P., then ${\alpha ^2},\;{\beta ^2},\;{\gamma ^2}$ are in
→
The value of a for which the matrix $A = \left( {\begin{array}{*{20}{c}}a&2\\2&4\end{array}} \right)$is singular if
→