dx x^2 + 4x + 13 is equal to - Vidyadip

MCQ

$\int {\frac{{dx}}{{{x^2} + 4x + 13}}} $ is equal to

A
$\log ({x^2} + 4x + 13) + c$
✓
$\frac{1}{3}{\tan ^{ - 1}}\left( {\frac{{x + 2}}{3}} \right) + c$
C
$\log (2x + 4) + c$
D
$\frac{{2x + 4}}{{{{({x^2} + 4x + 13)}^2}}} + c$

✓

Answer

Correct option: B.

$\frac{1}{3}{\tan ^{ - 1}}\left( {\frac{{x + 2}}{3}} \right) + c$

b
(b)$\int {\frac{{dx}}{{{x^2} + 4x + 13}} = \int {\frac{{dx}}{{{{(x + 2)}^2} + 9}} = \frac{1}{3}{{\tan }^{ - 1}}\frac{{(x + 2)}}{3} + 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

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

Similar questions

Let $f(x) = [2x^3 -5];$ then number of points in $(1, 2)$ where the function is discontinuous are where $[\,.]\, \to G.I.F$

The value of ${\sin ^2}{5^o} + {\sin ^2}{10^o} + {\sin ^2}{15^o} + ... + $ ${\sin ^2}{85^o} + {\sin ^2}{90^o}$ is equal to

The matrix $A = \left[ {\begin{array}{*{20}{c}}1&{ - 3}&{ - 4}\\{ - 1}&{\,\,\,3}&{\,\,4}\\1&{ - 3}&{ - 4}\end{array}} \right]$ is nilpotent of index

If $y' = \frac{{x - y}}{{x + y}}$, then its solution is

If in the equation $a{x^2} + bx + c = 0,$ the sum of roots is equal to sum of square of their reciprocals, then $\frac{c}{a},\frac{a}{b},\frac{b}{c}$ are in

For $0< c < b < a$, let $( a + b -2 c ) x ^2+( b + c -2 a ) x+(c+a-2 b)=0$ and $\alpha \neq 1$ be one of its root. Then, among the two statements
If $\alpha \in(-1,0)$ , then $b$ cannot be the geometric mean of $a$ and $c$
$(II)$ If $\alpha \in(0,1)$ , then $b$ may be the geometric mean of $a$ and $c$

The domain of the function $f(x) = \sqrt {x - {x^2}} + \sqrt {4 + x} + \sqrt {4 - x} $ is

If a right circularcone having maximum volume, is inscribed in a sphere of radius $3\, cm$, then the curved surface area (in $cm^2$) of this cone is

Solution of the differential equation

$x = 1 + xy\frac{{dy}}{{dx}} + \frac{{{{\left( {xy} \right)}^2}}}{{2!}}{\left( {\frac{{dy}}{{dx}}} \right)^2} + \frac{{{{\left( {xy} \right)}^3}}}{{3!}}{\left( {\frac{{dy}}{{dx}}} \right)^3} + ......$ is

A vector of magnitude $14 $ lies in the $xy-$ plane and makes an angle of ${60^o}$ with $x-$ axis. The components of the vector in the direction of $x-$ axis and $ y-$ axis are