Evaluate: 3x^2+1 (x^2-1)^3 dx - Vidyadip

MCQ

Evaluate: $\int\frac{3\text{x}^2+1}{(\text{x}^2-1)^3}\text{dx}$

✓
$\text{c}-\frac{\text{x}}{(\text{x}^2-1)^2}$
B
$\text{c}-\frac{\text{x}}{(\text{x}^2+1)^2}$
C
$\frac{\text{x}}{(\text{x}^2-1)^2}$
D
$\frac{\text{x}}{(\text{x}^2+1)^2}$

✓

Answer

Correct option: A.

$\text{c}-\frac{\text{x}}{(\text{x}^2-1)^2}$

$\text{c}-\frac{\text{x}}{(\text{x}^2-1)^2}$

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

Which of the following differential equations has $\text{y} = \text{c}_1\text{e}^\text{x} + \text{c}_2\text{e}^{-\text{x}}$ as the general solution?

The function $\text{f(x)}=\begin{cases}\frac{\text{x}^2}{\text{a}},&0\leq\text{x}<1\\\text{a},&1\leq\text{x}<\sqrt{2}\\\frac{2\text{b}^2-4\text{b}}{\text{x}^2},&\sqrt{2}\leq\text{x}<\infty\end{cases}$ is continuous for $0\leq\text{x}<\infty,$ then the most suitable values of $a$ and $b$ are:

The construction company uses concrete blocks made up of cement and sand. The weight of a concrete block has to be at least $5 kg$. Cement costs ₹ 20 per kg, while sand costs ₹ 6 per kg. Strength considerations dictate that the concrete block should contain minimum $4 kg$ of cement and not more than $2 kg$ of sand. Formulate the L.P.P for the cost to be minimum.

If the position vectors of the points $A, B, C$ be $a,\;b$, $3a - 2b$ respectively, then the points $A, B, C$ are

If ${A_i} = \left[ {\begin{array}{*{20}{c}}{{a^i}}&{{b^i}}\\{{b^i}}&{{a^i}}\end{array}} \right]$and if $|a|\, < 1,\,|b|\, < 1$, then $\sum\limits_{i = 1}^\infty {\det ({A_i})} $is equal to

Let $A = \,\left[ {\begin{array}{*{20}{c}}
1&0&0\\
1&1&0\\
1&1&1
\end{array}} \right]$ and $B = A^{20}$ . Then the sum of the elements of the first column of $B$ is?

A box contains coupons labelled $1,2,3, \ldots, n$. A coupon is picked at random and the number $x$ is noted. The coupon is put back into the box and a new coupon is picked at random. The new number is $y$.Then, the probability that one of the numbers $x, y$ divides the other is (in the options below $[r]$ denotes the largest integer less than or equal to $r$)

The vector $(\cos\text{a}\cos\beta)\hat{\text{i}}+(\cos\text{a}\sin\beta)\hat{\text{j}}+(\sin\text{a})\hat{\text{k}}$ is a:

Let $f (x)$ and $g (x)$ be two differentiable function in $R$ and $f(2) = 8, g (2) = 0, f (4) = 10$ and $g (4) = 8$ then

The minimum distance of a point on the curve $y = x^2 - 4$ from the origin is