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

MCQ

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

A
$\frac{1}{2}\,\,\,{\tan ^{ - 1}}\,\,\frac{{{x^2} + 2}}{{2x}}\,\, + \,\,C$
B
$\frac{1}{2}\,\,\,{\tan ^{ - 1}}\,\,({x^2} + 2)\, + \,\,C$
C
$\frac{1}{2}\,\,\,{\tan ^{ - 1}}\,\,\frac{{2x}}{{{x^2} - 2}}\,\, + \,\,C$
✓
$\frac{1}{2}\,\,\,{\tan ^{ - 1}}\,\,\frac{{{x^2} - 2}}{{2x}}\,\, + \,\,C$

✓

Answer

Correct option: D.

$\frac{1}{2}\,\,\,{\tan ^{ - 1}}\,\,\frac{{{x^2} - 2}}{{2x}}\,\, + \,\,C$

d

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 $f:[1, \infty) \rightarrow[2, \infty)$ be a differentiable function such that $f(1)=2$. If $6 \int_1^x f(t) d t=3 x f(x)-x^3$ for all $x \geq 1$, then the value of $f(2)$ is

If $P$ & $Q$ are two non-singular matrices of the same order such that $Q^r = I$ , for some integer $r > 1$ , then $P^{-1}Q^{r-1}P -P^{-1}Q^{-1}P$ is equal to (where $I$ is identity matrix and $O$ is null matrix)

$\sin {20^o}\,\sin {40^o}\,\sin {60^o}\,\sin {80^o} = $

Football teams $T_1$ and $T_2$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $T_1$ winning, drawing and losing a game against $T_2$ are $\frac{1}{2}, \frac{1}{6}$ and $\frac{1}{3}$, respectively. Each team gets $3$ points for a win, $1$ point for a draw and $0$ point for a loss in a game. Let $X$ and $Y$ denote the total points scored ky teams $T_1$ and $T_2$, respectively, after two games.

($1$) $P(X>Y)$ is

($A$) $\frac{1}{4}$ ($B$) $\frac{5}{12}$ ($C$) $\frac{1}{2}$ ($D$) $\frac{7}{12}$

($2$) $P(X=Y)$ is

($A$). $\frac{11}{36}$ ($B$) $\frac{1}{3}$ ($C$) $\frac{13}{36}$ ($D$) $\frac{1}{2}$

Given the answer quetion ($1$) and ($2$)

If the number of terms in the expansion of ${\left( {1 - \frac{2}{x} + \frac{4}{{{x^2}}}} \right)^n},x \ne 0$ is $28$ then the sum of the coefficients of all the terms in this expansion, is :

Tangents are drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$, parallel to the straight line $2 x-y=1$. The points of contacts of the tangents on the hyperbola are

$(A)$ $\left(\frac{9}{2 \sqrt{2}}, \frac{1}{\sqrt{2}}\right)$ $(B)$ $\left(-\frac{9}{2 \sqrt{2}},-\frac{1}{\sqrt{2}}\right)$

$(C)$ $(3 \sqrt{3},-2 \sqrt{2})$ $(D)$ $(-3 \sqrt{3}, 2 \sqrt{2})$

Let $C$ be a circle with radius $\sqrt{10}$ units and centre at the origin. Let the line $x + y = 2$ intersects the circle $C$ at the points $P$ and $Q$. Let $MN$ be a chord of $C$ of length $2$ unit and slope $-1$. Then, a distance $($in units$)$ between the chord $PQ$ and the chord $MN$ is

$\int {\frac{{\log x -log^2\ x+ x^2}}{{{x^3}}}} dx\,\,is\, $ (where $C$ is constant of integration)

Number of solutions of the equation $2tan^{-1}(cos^2x) = tan^{-1}(2cosec^2x)$ in $\left[ {0,5\pi } \right]$ is $m$ , then

$\int_{\,0}^{\,\pi } {{e^{{{\sin }^2}x}}{{\cos }^3}x\,dx} $ is equals to