_ ^ [ ( x) + 1 ( x) ^2 ] ;dx = - Vidyadip

MCQ

$\int_{}^{} {\left[ {\log (\log x) + \frac{1}{{{{(\log x)}^2}}}} \right]} \;dx = $

A
$x\log (\log x) + \frac{x}{{\log x}} + c$
✓
$x\log (\log x) - \frac{x}{{\log x}} + c$
C
$x\log (\log x) + \frac{{\log x}}{x} + c$
D
$x\log (\log x) - \frac{{\log x}}{x} + c$

✓

Answer

Correct option: B.

$x\log (\log x) - \frac{x}{{\log x}} + c$

b
(b)$\int_{}^{} {\left[ {\log (\log x) + \frac{1}{{{{(\log x)}^2}}}} \right]\,dx} = \int_{}^{} {\log (\log x)dx + \int_{}^{} {\frac{1}{{{{(\log x)}^2}}}} } dx$
$ = x\log (\log x) - \int_{}^{} {\frac{x}{{x\log x}}\,dx + \int_{}^{} {\frac{1}{{{{(\log x)}^2}}}dx} } $
$ = x\log (\log x) - \frac{x}{{\log x}} - \int_{}^{} {\frac{1}{{{{(\log x)}^2}}}dx + \int_{}^{} {\frac{1}{{{{(\log x)}^2}}}dx} } $
$ = x\log (\log x) - \frac{x}{{\log x}} + 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

If by dropping a stone in a quiet lake a wave moves in circle at a speed of $3.5 \,cm/sec,$ then the rate of increase of the enclosed circular region when the radius of the circular wave is $10$ $cm,$ is ......... $c{m^2}/sec$. $\left( {\pi = {{22} \over 7}} \right)$

$\mathop {Lim}\limits_{n \to \infty } $$\frac{\pi }{{2\,n}}\,\,\left( {1\,\, + \,\,\cos \,\frac{\pi }{{2\,n}}\,\, + \,\,\cos \,\frac{{2\,\pi }}{{2\,n}}\,\, + \,\,.....\,\, + \,\,\cos \,\frac{{(n\, - \,1)\,\pi }}{{2\,n}}} \right)$ equal to

If $x$ satisfies the equation $\left( {\int\limits_0^1 {\frac{{dt}}{{{t^2} + 2t\cos \alpha + 1}}} } \right)\,{x^2}$ $-$ $\,\left( {\int\limits_{ - 3}^3 {\frac{{{t^2}\sin 2t}}{{{t^2} + 1}}\,dt} } \right)\,x$ $-$ $2$ $ =$ $ 0 (0 < \alpha < \pi ), $ then the value $x$ is

In a binomial distribution $B ( n , p )$, the sum and product of the mean and variance are $5$ and $6$ respectively, then find $6(n+p-q)$ is equal to :-

The direction cosines of the vector $3i - 4j + 5k$ are

Let, $\quad f(x)=\left\{\begin{array}{cc}\frac{x}{\sin x}, & x \in(0,1) \\ 1, & x=0\end{array}\right.$ Consider the integral $I_n=\sqrt{n} \int_0^{1 / n} f(x) e^{-n x} d x$ . Then, $\lim _{n \rightarrow \infty} I_n$

If the constraints in a linear programming problem are changed:

Solution is not defined.
The objective function has to be modified.
The problems is to be re - evaluated.
None of these.

If $f(x) = {x^3} - 6{x^2} + 9x + 3$ be a decreasing function, then $x $ lies in

The area bounded by the curve $\text{y}=\log_{\text{e}}\text{x}$ and x-axis and the straight line x = e is:

$\text{e sq. units}$
$1\text{ sq. units}$
$1-\frac{1}{\text{e}}\text{ sq. units}$
$1+\frac{1}{\text{e}}\text{ sq. units}$

For $x \in R$, two real valued functions $f(x)$ and $g(x)$ are such that, $g(x)=\sqrt{x}+1$ and $f o g(x)=x+3-\sqrt{x}$. Then $f(0)$ is equal to