d x x^ 2 +2 x+2 equals - Vidyadip

Question

$\int \frac{d x}{x^{2}+2 x+2}$ equals

✓

Answer

$\int \frac{d x}{x^{2}+2 x+2}=\int \frac{d x}{\left(x^{2}+2 x+1\right)+1}$
$= \int \frac{1}{(x+1)^{2}+(1)^{2}} d x$
$=\left[\tan ^{-1}(x+1)\right]+C$

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 "1 Marks Question" from Integrals→Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\text{y}=\text{px}+\sqrt{\text{a}^2\text{p}^2+\text{b}^2},$ where $\text{p}=\frac{\text{dy}}{\text{dx}}$

Find the magnitude of each of the two vectors $\vec{\text{a}}\ \text{and}\ \vec{\text{b}},$ having the same magnitude such that the angle between them is 60° and their scalar product is $\frac{9}{2}.$

Sand is pouring from a pipe at the rate of $12cm^3/s$. the falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is $4 cm$?

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\frac{\text{d}^3\text{y}}{\text{dx}^3}+\Big(\frac{\text{d}^2\text{y}}{\text{dx}^2}\Big)+\frac{\text{dy}}{\text{dx}}+4\text{y}=\sin\text{x}$

If $\ \begin{bmatrix}2\text{x} & 5\\8 & \text{x}\\\end{bmatrix} \ = \ \begin{bmatrix}6 & -2\\7 & 3\\\end{bmatrix}, \ $ , Write the value of x.

Let R be a relation on the set A of ordered pairs of positive integers defined by
(x, y) R (u, v) if and only if xv = yu.
Show that R is an equivalence relation.

Coloured balls are distributed in four boxes as shown in the following table:

Box	Colour
Box	Black	White	Red	Blue
$I$	$3$	$4$	$5$	$6$
$II$	$2$	$2$	$2$	$2$
$III$	$1$	$2$	$3$	$1$
$IV$	$4$	$3$	$1$	$5$

A box is selected at random and then a ball is randomly drawn from the selected box. The colour of the ball is black, what is the probability that ball drawn is from the box $III?$

If $\vec a$ is a non zero vector of magnitude ‘a’ and $\lambda $ a non zero scalar, then $\lambda \vec a$ is a unit vector if

If P(A) = $\frac{1}{2}$, P(B) = 0, then P(A|B) is

A coin is tossed three times, determine P(E|F),
where E: at least two heads, F: at most two heads.