Download App

Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
The value of $\int\frac{1}{\text{x}+\text{x}\log\text{x}}\text{ dx}$ is:
  • A
    $1+\log\text{x}$
  • B
    $\text{x}+\log\text{x}$
  • C
    $\text{x}\log\text{x}(1+\log\text{x})$
  • ✓
    $\log(1+\log\text{x})$
✓

Answer

Correct option: D.
$\log(1+\log\text{x})$
$\text{I}=\int\frac{1}{\text{x}+\text{x}\log\text{x}}\text{ dx}$
$\text{I}=\int\frac{\text{dx}}{\text{x}+(1+\log\text{x})}$
Put $1+\log\text{x}=\text{t}$
$\frac{1}{\text{x}}\text{dx}=\text{dt}$
$\text{I}=\int\frac{1}{\text{t}}\text{ dt}$
$\text{I}=\log|\text{t}|+\text{C}$
$\text{I}=\log(1+\log\text{x})+\text{C}$

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 "M.C.Q (1 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

If the system of equations $x + y+  z = 5$ ; $x + 2y + 3z = 9$ ; $x + 3y + \alpha z = \beta $ has infinitely many solutions, then $\beta  - \alpha $ equals
→
The area (in $sq. units$) of the region $A = \left\{ {\left( {x,y} \right):\frac{{{y^2}}}{2} \le x \le y + 4} \right\}$ is
→
If the area of the region $\left\{(x, y): 0 \leq y \leq \min \left\{2 x, 6 x-x^2\right\}\right\}$ is $A$, then $12 A$ is equal to
→
The value of $\int \frac{1}{\sin ^2 x \cdot \cos ^2 x} d x$ is
→
For which value of $x$, are the determinants $\left|\begin{array}{cc}2 x & -3 \\ 5 & x \end{array}\right|$ and $\left|\begin{array}{rr}10 & 1 \\ -3 & 2\end{array}\right|$ equal?
→
The point $(0,\,5)$ is closest to the curve ${x^2} = 2y$ at
→
The area (in sq. units) of the region described by $\left\{(\mathrm{x}, \mathrm{y}): \mathrm{y}^2 \leq 2 \mathrm{x}\right.$, and $\left.\mathrm{y} \geq 4 \mathrm{x}-1\right\}$ is
→
Let $f: R \rightarrow R$ be defined as

$f(x)=\left\{\begin{array}{cc}2 \sin \left(-\frac{\pi x}{2}\right), & \text { if } x<-1 \\ \left|a x^{2}+x+b\right|, & \text { if }-1 \leq x \leq 1 \\ \sin (\pi x), & \text { if } x>1\end{array}\right.$

If $f(x)$ is continuous on $R,$ then $a+b$ equals ..... .

→
$\int\sin^{-1}\text{xdx}$ is equal to:
→
lf $x + \left| y \right| = 2y,$ then $y$ as a function of $x,$ at $x = 0$ is
→