2x (1+x^2) 1+x^2 dx: - Vidyadip

MCQ

$\int\frac{2\text{x}\log(1+\text{x}^2)}{1+\text{x}^2}\text{dx:}$

A
$\log(1+\text{x}^2)+\text{c}$
✓
$\frac{[\log(1+\text{x}^2)^2]}{2}+\text{c}$
C
$2\log(1+\text{x}^2)+\text{c}$
D
None of these

✓

Answer

Correct option: B.

$\frac{[\log(1+\text{x}^2)^2]}{2}+\text{c}$

$\int\frac{2\text{x}\log(1+\text{x}^2)}{1+\text{x}^2}\text{dx}$
Let $\log(1+\text{x}^2) =\text{z}$ and $\frac{\text{2x}}{1+\text{x}^2}\text{dx}=\text{dz}$ Using these in the above integration we get,
$=\int\text{z, }{\text{dz}}$
$\frac{\text{z}^2}{2}+\text{c}\ [$Where $c$ is integrating constant$]$
$=\frac{[\log(1+\text{x}^2)^2]}{2}+\text{c}$

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 $X$ is a random variable with probability distribution as given below :

$X = x_i$	$0$	$1$	$2$	$3$
$P(X = X_i)$	$k$	$3k$	$3k$	$k$

The value of $k$ and its variance are :

$\mathop {Lim}\limits_{n \to \infty } \,\,\sum\limits_{k = 1}^n {\frac{n}{{{n^2} + {k^2}{x^2}}}} $,$ x > 0$ is equal to

Choose the correct answer from given four options in each of the Exercise: The determinant $\begin{vmatrix}\text{b}^2-\text{ab}&\text{b}-\text{c}&\text{bc}-\text{ac}\\\text{ab}-\text{a}^2&\text{a}-\text{b}&\text{b}^2-\text{ab}\\\text{bc}-\text{ac}&\text{c}-\text{a}&\text{ab}-\text{a}^2\end{vmatrix}$ equals to:

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

If the determinant $\left| {\begin{array}{*{20}{c}}{a\, + \,p}&{1\, + \,x}&{u\, + \,f}\\ {b\, + \,q}&{m\, + \,y}&{v\, + \,g}\\{c\, + \,r}&{n\, + \,z}&{w\, + \,h}\end{array}} \right|$ splits into exactly $K$ determinants of order $3$, each element of which contains only one term, then the value of $K$, is

A bag contains $4$ white and $6$ black balls. Three balls are drawn at random from the bag. Let $X$ be the number of white balls, among the drawn balls. If $\sigma^{2}$ is the variance of $X$, then $100 \sigma^{2}$ is equal to.

If $A$ and $ B$ are two square matrices such that $B = - {A^{ - 1}}BA$, then ${(A + B)^2} = $

The value of $\lambda$ for which two vectors $2 \hat{i}-\hat{j}+2 \hat{k}$ and $3 \hat{i}+\lambda \hat{j}+\hat{k}$ are perpendicular is

Choose the correct answer from the given four option.
The differential equation of the family of curves $\text{x}^2+\text{y}^2-2\text{ay}=0,$ where a is arbitrary constant, is:

If $f(x) = \left\{ \begin{array}{l}\,\,\,\,\,\,\,\,\,\,\,\,\,\,1,\,{\rm{when\,\,}}\,\,0 < x \le \frac{{3\pi }}{4}\\2\sin \frac{2}{9}x,{\rm{when\,\,}}\,\frac{{3\pi }}{4} < x < \pi \end{array} \right.$, then