If _ ^ ( x^2 + x)dx = x ( x^2 + x) + A , then A = - Vidyadip

MCQ

If $\int_{}^{} {\ln ({x^2} + x)dx = x\ln ({x^2} + x) + A} $, then $A = $

A
$2x + \ln (x + 1) + $constant
B
$2x - \ln (x + 1) + $constant
C
Constant
✓
None of these

✓

Answer

Correct option: D.

None of these

d
(d)$\int_{}^{} {\log ({x^2} + x)\,dx} = \int_{}^{} {\log x\,dx} + \int_{}^{} {\log (x + 1)\,dx} $
$ = x\log x - x + x\log (x + 1) - x + \log (x + 1)$
$ = x\left\{ {(\log x + \log (x + 1)} \right\} - 2x + \log (x + 1)$
$ = x\log ({x^2} + x) - 2x + \log (x + 1)$
Equating it to the given integration, we get
$A = - 2x + \log (x + 1)$.

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 man of height $2$ $metres$ walks at a uniform speed of $5\ km/hr$. away from a lamp post which is $6$ $metres$ high. Find the rate at which the length of his shadow increases ........... $km/hr$.

If complex numbers $z_1$, $z_2$ are such that $\left| {{z_1}} \right| = \sqrt 2 ,\left| {{z_2}} \right| = \sqrt 3$ and $\left| {{z_1} + {z_2}} \right| = \sqrt {5 - 2\sqrt 3 }$, then the value of $|Arg z_1 -Arg z_2|$ is

If position vectors of a point $A$ is $a + 2b$ and a divides $ AB $ in the ratio $2:3$, then the position vector of $ B$ is

The acute angle between the line joining the points $(2,1,-3), (-3,1,7)$ and a line parallel to $\frac{{x - 1}}{3} = $ $\frac{y}{4} = \frac{{z + 3}}{5}$ through the point $(-1, 0, 4)$ is

$\int_{}^{} {{a^x}\;da = } $

If $\int {} e^u$ . $\sin 2x dx$ can be found in terms of known functions of $x$ then $u$ can be :

$1 + \frac{1}{4} + \frac{{1.3}}{{4.8}} + \frac{{1.3.5}}{{4.8.12}} + ........... = $

If $x = a + b,y = a\alpha + b\beta $ and $z = a\beta + b\alpha ,$ where $\alpha $and $\beta $ are complex cube roots of unity, then $xyz$ =

$\int_{\,0}^{\,2\pi } {|\sin x|\,dx = } $

The co-ordinates axes are rotated through an angle $135^o$. If the coordinates of a point $P$ in the new system are known to be $(4, -3)$, then the coordinates of $P$ in the original system are