_ ^ x^2 + x - 6 (x - 2)(x - 1) dx = - Vidyadip

MCQ

$\int_{}^{} {\frac{{{x^2} + x - 6}}{{(x - 2)(x - 1)}}dx = } $

A
$x + 2\log (x - 1) + c$
B
$2x + 2\log (x - 1) + c$
C
$x + 4\log (1 - x) + c$
✓
$x + 4\log (x - 1) + c$

✓

Answer

Correct option: D.

$x + 4\log (x - 1) + c$

d
(d)$\int_{}^{} {\frac{{{x^2} + x - 6}}{{(x - 2)(x - 1)}}\,dx} = \int_{}^{} {\frac{{(x + 3)(x - 2)}}{{(x - 2)(x - 1)}}\,dx} = \int_{}^{} {\frac{{x + 3}}{{x - 1}}\,dx} $
$ = \int_{}^{} {\frac{{x - 1}}{{x - 1}}\,dx + \int_{}^{} {\frac{4}{{x - 1}}\,dx} } = x + 4\log (x - 1) + c$.

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

More "M.C.Q (1 Marks)" from 7.1 inderfinite integral→7.1 inderfinite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $A$ and $B$ are two matrices such that $AB = B$ and $BA = A,$ then ${A^2} + {B^2} = $

The lines $\frac{\text{x}}{1}=\frac{\text{y}}{2}=\frac{\text{z}}{3}$ and $\frac{\text{x}-1}{-2}=\frac{\text{y}-2}{-4}=\frac{\text{z}-3}{-6}$ are:

Parallel.
Intersecting.
Skew.
Coincident.

The sine of the angle between the straight line $\frac{\text{x}-2}{3}=\frac{\text{y}-3}{4}=\frac{\text{z}-4}{5}$ and the plane 2x - 2y + z = 5 is:

$\frac{10}{6\sqrt{5}}$
$\frac{4}{5\sqrt{2}}$
$\frac{2\sqrt{3}}{5}$
$\sqrt{\frac{\sqrt{2}}{10}}$

The area (in sq. units) of the largest rectangle $ABCD$ whose vertices $A$ and $B$ lie on the $x$-axis and vertices $C$ and $D$ lie on the parabola, $y = x ^{2}-1$ below the $x$ -axis, is

Let f : R → R be given by $\text{f(x)}=\tan\text{x}.$ Then, f^-1(1) is:

$\frac{\pi}{4}$
$\big\{\text{n}\pi+\frac{\pi}{4}:\text{n}\in\text{Z}\big\}$
Does not exist.
None of these.

$\int {\frac{{1 - {x^7}}}{{x\left( {1 + {x^7}} \right)}}} \,dx$ equals

The equation of a line passing through the point $(-3,2,-4)$ and equally inclined to the axes are

In a box containing 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs, none is defective?

$\big(\frac{9}{10}\big)^5$
$\frac{9}{10}$
$10^{-5}$
$\big(\frac{1}{2}\big)^2$

The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{x^2 \cos x}{1+e^x} d x$ is equal to

If $\tan ({\cos ^{ - 1}}x) = \sin \left( {{{\cot }^{ - 1}}\frac{1}{2}} \right)$, then $x =$