_ ^ x + 1 1 + x^2 dx = - Vidyadip

MCQ

$\int_{}^{} {\frac{{x + 1}}{{\sqrt {1 + {x^2}} }}dx} = $

A
$\sqrt {1 + {x^2}} + {\tan ^{ - 1}}x + c$
B
$\sqrt {1 + {x^2}} - \log \{ x + \sqrt {1 + {x^2}} \} + c$
✓
$\sqrt {1 + {x^2}} + \log \{ x + \sqrt {1 + {x^2}} \} + c$
D
$\sqrt {1 + {x^2}} + \log (\sec x + \tan x) + c$

✓

Answer

Correct option: C.

$\sqrt {1 + {x^2}} + \log \{ x + \sqrt {1 + {x^2}} \} + c$

c
(c)$\int_{}^{} {\frac{{x + 1}}{{\sqrt {{x^2} + 1} }}\,dx = \int_{}^{} {\frac{x}{{\sqrt {{x^2} + 1} }}\,dx + \int_{}^{} {\frac{1}{{\sqrt {{x^2} + 1} }}\,dx} } } $
Put ${x^2} + 1 = t \Rightarrow 2x\,dx = dt$, then it reduce to $\frac{1}{2}\int_{}^{} {\frac{{dt}}{{{t^{1/2}}}} + \int_{}^{} {\frac{1}{{\sqrt {{x^2} + 1} }}} } \,dx = \frac{1}{2}.2.{t^{1/2}} + \log (x + \sqrt {{x^2} + 1} ) + c$
$ = {({x^2} + 1)^{1/2}} + \log (x + \sqrt {{x^2} + 1} ) + 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 7.1 inderfinite integral→7.1 inderfinite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least $0.96$ is

If ${I_n} = \int_0^{\pi /4} {{{\tan }^n}\theta \,d\theta ,} $ then ${I_8} + {I_6}$ equals

Let $A= \{1, 2, 3, 4\}$ and $R : A \to A$ be the relation defined by $R = \{ (1, 1), (2, 3), (3, 4), ( 4, 2) \}$. The correct statement is

If $\int {} e^u$ . $\sin 2x dx$ can be found in terms of known functions of $x$ then $u$ can be :

The set points where the function f(x) given by $\text{f(x)=}|\text{x}-3|\cos\text{x}$ is diffrentiable, is:

R
R - {3}
$(0,\infty)$
None of these.

If $\vec{\text{a}}=2\hat{\text{i}}-3\hat{\text{j}}-\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}+4\hat{\text{j}}-2\hat{\text{k}},$ then $\vec{\text{a}}\times\vec{\text{b}}$ is:

$10\hat{\text{i}}+2\hat{\text{j}}+11\hat{\text{k}}$
$10\hat{\text{i}}+3\hat{\text{j}}+11\hat{\text{k}}$
$10\hat{\text{i}}-3\hat{\text{j}}+11\hat{\text{k}}$
$10\hat{\text{i}}-2\hat{\text{j}}-10\hat{\text{k}}$

If $\hat{\text{i}},\hat{\text{j}},\hat{\text{k}}$ are unit vectors, then

$\hat{\text{i}}.\hat{\text{j}}=1$
$\hat{\text{i}}.\hat{\text{i}}=1$
$\hat{\text{i}}\times\hat{\text{j}}=1$
$\hat{\text{i}}\times\big(\hat{\text{j}}\times\hat{\text{k}}\big)=1$

If $f(x) = \left\{ {\begin{array}{*{20}{c}}{4x + 3\,,}&{{\rm{if}}}&{1 \le x \le 2}\\{3x + 5\,,}&{{\rm{if}}}&{2 < x \le 4}\end{array}} \right.$ then $\int_1^4 {\,f(x)} \,dx = $

The value of $\int\limits_{ - 1}^1 {\frac{{dx}}{{\sqrt {\,|\,x\,|} }}} \,\,$ is

Domain of function $f(x) = log|5{x} - 2x|$ is $x \in R - A$, then $n(A)$ is (where $\{.\}$ denotes fractional part function)