_ ^ x ;dx x^3 = - Vidyadip

MCQ

$\int_{}^{} {\frac{{\log x\;dx}}{{{x^3}}} = } $

A
$\frac{1}{{4{x^2}}}(2\log x - 1) + c$
✓
$ - \frac{1}{{4{x^2}}}(2\log x + 1) + c$
C
$\frac{1}{{4{x^2}}}(2\log x + 1) + c$
D
$\frac{1}{{4{x^2}}}(1 - 2\log x) + c$

✓

Answer

Correct option: B.

$ - \frac{1}{{4{x^2}}}(2\log x + 1) + c$

b
(b)$\int_{}^{} {\frac{{\log x}}{{{x^3}}}dx = \int_{}^{} {{x^{ - 3}}\log x\;dx} } $
$ = - \frac{{\log x}}{{2{x^2}}} + \int_{}^{} {\frac{1}{x}.\frac{1}{{2{x^2}}} + c = - \frac{{\log x}}{{2{x^2}}} + \frac{1}{2}.\frac{{{x^{ - 2}}}}{{ - 2}} + c} $
$ = - \frac{{\log x}}{{2{x^2}}} - \frac{1}{{4{x^2}}} + c = - \frac{1}{{4{x^2}}}(2\log x + 1) + 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 STD 12 - 7.1 inderfinite integral→STD 12 - 7.1 inderfinite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The function $\text{f}(\text{x})=2\log(\text{x}-2)-\text{x}^2+4\text{x}+1$ increases on the interval:

Let $f$ be a real-valued differentiable function on $R$ (the set of all real numbers) such that $f(1)=1$. If the $y$ intercept of the tangent at any point $P(x, y)$ on the curve $y=f(x)$ is equal to the cube of the abscissa of $P$, then the value of $f(-3)$ is equal to

Let $g(x)$ be the inverse of the function $f(x)$ and $f'(x) = {1 \over {1 + {x^3}}}$. Then $g'(x)$ is equal to

Let $A = \left( {\begin{array}{*{20}{c}}1&{ - 1}&1\\2&1&{ - 3}\\1&1&1\end{array}} \right)$ and $(10)B = \left( {\begin{array}{*{20}{c}}4&2&2\\{ - 5}&0&\alpha \\1&{ - 2}&3\end{array}} \right)$. If $B$ is the inverse of matrix $A$, then $\alpha $ is

If A = [1 amp; 2], B = [3 amp; 4] then A + B =

$\left| {\,\begin{array}{*{20}{c}}{1/a}&1&{bc}\\{1/b}&1&{ca}\\{1/c}&1&{ab}\end{array}\,} \right| = $

For the binary operation * defined on R − {1} by the rule a * b = a + b + ab for all a, b ∈ R − {1}, the inverse of a is:

If $\frac{\text{dy}}{\text{dx}}=\text{e}^{-2\text{y}}$ and $y = 0,$ when $x = 5,$ then the value of $x$ when $y = 3$ is:

Let $A = \{ 2,\,4,\,6,\,8\} $. $A$ relation $R$ on $A$ is defined by $R = \{ (2,\,4),\,(4,\,2),\,(4,\,6),\,(6,\,4)\} $. Then $R$ is

The ratio of the areas between the curves $\text{y}=\cos\text{x}$ and $\text{y}=\cos2\text{x}$ and $x-$ axis from $x = 0$ to $x = 0$ to $\text{x}=\frac{\pi}{3}$