_ ^ 1 x^2 ( x^2 + a^2 )dx = - Vidyadip

MCQ

$\int_{}^{} {\frac{1}{{{x^2}}}\log ({x^2} + {a^2})dx = } $

A
$\frac{1}{x}\log ({x^2} + {a^2}) + \frac{2}{a}{\tan ^{ - 1}}\frac{x}{a} + c$
✓
$ - \frac{1}{x}\log ({x^2} + {a^2}) + \frac{2}{a}{\tan ^{ - 1}}\frac{x}{a} + c$
C
$ - \frac{1}{x}\log ({x^2} + {a^2}) - \frac{2}{a}{\tan ^{ - 1}}\frac{x}{a} + c$
D
None of these

✓

Answer

Correct option: B.

$ - \frac{1}{x}\log ({x^2} + {a^2}) + \frac{2}{a}{\tan ^{ - 1}}\frac{x}{a} + c$

b
(b) $\int_{}^{} {\frac{1}{{{x^2}}}\log ({x^2} + {a^2})\,dx} = \int_{}^{} {{x^{ - 2}}\log ({x^2} + {a^2})\,dx} $
$ = \frac{{ - \log ({x^2} + {a^2})}}{x} + \int_{}^{} {\frac{{2x}}{{({x^2} + {a^2})}}.\frac{1}{x} + c} $
$ = \frac{{ - \log ({x^2} + {a^2})}}{x} + \frac{2}{a}{\tan ^{ - 1}}\frac{x}{a} + 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 "M.C.Q (1 Marks)" from STD 12 - 7.1 inderfinite integral→STD 12 - 7.1 inderfinite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Find the identity element in the set $I^+$ of all positive integers defined by $a \times b = a + b$ for all $a, b \in I^+.$

$\int_{}^{} {\frac{{{x^5}\;dx}}{{\sqrt {(1 + {x^3})} }} = } $

The number of solution of the following equations ${x_2} - {x_3} = 1,\,\, - {x_1} + 2{x_3} = - 2,$ ${x_1} - 2{x_2} = 3$ is

The solution of the differential equartion $\frac{\text{dy}}{\text{dx}}-\frac{\text{y}(\text{x}+1)}{\text{x}}=0$ is given by:

If $a = i - 2j + 3k$ and $b = 3i + j + 2k,$ then the unit vector perpendicular to $a$ and $b$ is

If the position vectors of the vertices of a triangle be $6i + 4j + 5k,\,\,\,4i + 5j + 6k$ and $5i + 6j + 4k,$ then the triangle is

The corner points of the feasible region determined by the system of linear inequalities are (0, 0), (4, 0), (2, 4) and (0, 5). If the maximum value of z = ax + by, where a, b > 0 occurs at both (2, 4) and (4, 0), then:

If x, y, z are non-zero real numbers, then the inverse, then the inverse of the matrix $\begin{bmatrix}\text{x} & 0 & 0\\ 0 & \text{y} & 0 \\ 0 & 0 & \text{z}\end{bmatrix}$, is:

Let $A =\{1,2,3,4, \ldots .10\}$ and $B =\{0,1,2,3,4\}$ The number of elements in the relation $R =\{( a , b )$ $\left.\in A \times A : 2( a - b )^2+3( a - b ) \in B \right\}$ is $.........$.

The relation 'R' in N × N such that (a, b)R(c, d) ⇔ a + d = b + c is: