Integrate the functions in Exercises: 1 (2-x)^2 +1 - Vidyadip

Question

Integrate the functions in Exercises:
$\frac{1}{\sqrt{(2-\text{x})^2}+1}$

✓

Answer

$\int\frac{1}{\sqrt{(2-\text{x})^2}+1}\text{ dx}$
$=\frac{\log\bigg|(2-\text{x})+\sqrt{(2-\text{x})^2+1^2}\bigg|}{-1\rightarrow\text{Coeff. of x}}+\text{c}$$ \ \ \ \ \ \ \ \bigg[\because\int\frac{1}{\sqrt{\text{x}^2+\text{a} ^2}}\text{ dx}=\log\bigg|\text{x}+\sqrt{\text{x}^2+\text{a}^2}\bigg|\bigg]$
$=-\log\bigg|2-\text{x}+\sqrt{4+\text{x}^2-4\text{x}+1}\bigg|+\text{c}$
$=\log\Bigg|\frac{1}{2-\text{x}\sqrt{\text{x}^2-4\text{x}+5}}\Bigg|+\text{C}$

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 "2 Marks" 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

Evaluate the following determinant:
$\begin{vmatrix}1&4&9\\4&9&16\\9&16&25 \end{vmatrix}$

For the set A = {1, 2, 3}, define a relation R on the set A as follows:
R = {(1, 1), (2, 2), (3, 3), (1, 3)}
Write the ordered pairs to be added to R to make the smallest equivalence relation.

A vector $\vec{\text{r}}$ is inclined at equal acute angles to x-axis, y-axis and z-axis. If $|\vec{\text{r}}|=6$ units, find $\vec{\text{r}}$.

Find the equation of the plane which contains the line of intersection of the planes $\vec{r} \cdot(\hat{i}+2 \hat{j}+3 \hat{k})-4=0, \quad \vec{r} \cdot(2 \hat{i}+\hat{j}-\hat{k})+5=0$ and which is perpendicular to the plane $\vec{r} \cdot(5 \hat{i}+3 \hat{j}-6 \hat{k})+8=0$.

If A is a square matrix such that A (adj A) = 5I, where I denotes the identity matrix of the same order. Then, find the value of |A|.

If f : C → C is defined by f(x) = x², write f^-1(-4). Here, C denotes the set of all complex numbers.

Let *′ be the binary operation on the set {1, 2, 3, 4, 5} defined by a *' b = H.C.F. of a and b. Is the operation *′ same as the operation * defined in Exercise 4 above? Justify your answer.

Find $\frac{d^{2} y}{d x^{2}}$, if y = x³ + tan x.

Two cards are drawn from a well shuffled pack of 52 cards, one after another without replacement. Find the probability that one of these is red card and the other a black card?

If $\cos^{-1}\text{x}+\cos^{-1}\text{y}=\frac{\pi}{4},$ find the value of $\sin^{-1}\text{x}+\sin^{-1}\text{y}$