If x^3dx 1+x^2 =a(1+x^2)^ 3 2 +b 1+x^2 +c, then: - Vidyadip

MCQ

If $\int\frac{\text{x}^3\text{dx}}{\sqrt{1+\text{x}^2}}=\text{a}(1+\text{x}^2)^{\frac{3}{2}}+\text{b}\sqrt{1+\text{x}^2}+\text{c,}$ then:

A
$\text{a}=\frac{1}{3},\text{b}=1$
B
$\text{a}=\frac{-1}{3},\text{b}=1$
C
$\text{a}=\frac{-1}{3},\text{b}=-1$
✓
$\text{a}=\frac{1}{3},\text{b}=-1$

✓

Answer

Correct option: D.

$\text{a}=\frac{1}{3},\text{b}=-1$

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

The value of $\int\frac{\cos2\text{x}}{{\cos}{\text{ x}}}\text{dx}$ is equal to:

The maximum possible area bounded by the parabola $y=x^2+x+10$ and a chord of the parabola of length $1$ is

Order of $\Big(\frac{\text{dy}}{\text{dx}}+3\text{x}\Big)^\frac{3}{2}=\text{x}+\frac{3\text{dy}}{\text{dx}}$ is:

If $x, y, z$ are not all simultaneously equal to zero, satisfying the system of equations

($\sin 3 \theta ) x - y + z = 0$
($\cos 2 \theta ) x + 4 y + 3 z = 0$
$2 x + 7 y + 7 z = 0$
then the number of principal values of $\theta$ is

A function $f(x)$ is given by $f(x)=\frac{5^{x}}{5^{x}+5}$, then the sum of the series

$f\left(\frac{1}{20}\right)+f\left(\frac{2}{20}\right)+f\left(\frac{3}{20}\right)+\ldots \ldots+f\left(\frac{39}{20}\right)$ is equal to ....... .

Let $R =\{ a , b , c , d , e \}$ and $S =\{1,2,3,4\}$. Total number of onto function $f: R \rightarrow S$ such that $f(a) \neq$ 1 , is equal to $.............$.

Two vectors $\vec{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k}$ and $\vec{b}=b_1 \hat{i}+b_2 \hat{j}+b_3 \hat{k}$ are collinear if

Solve the system of the following equations $\frac{2}{x}+\frac{3}{y}+\frac{10}{z}=4$ ; $\frac{4}{x}-\frac{6}{y}+\frac{5}{z}=1$ ; $\frac{6}{x}+\frac{9}{y}-\frac{20}{z}=2$

$\int\limits_2^3 {\frac{{{{(x + 2)}^2}}}{{2{x^2} - 10x + 53}}} dx = $

Let $y = y _1( x )$ and $y = y _2( x )$ be the solution curves of the differential equation $\frac{d y}{d x}=y+7$ with initial conditions $y_1(0)=0, y_2(0)=1$ respectively. Then the curves $y=y_1(x)$ and $y=y_2(x)$ intersect at