x^3 x , ,dx = - Vidyadip

MCQ

$\int {{x^3}\log x\,\,dx = } $

A
$\frac{{{x^4}\log x}}{4} + c$
✓
$\frac{1}{{16}}[4{x^4}\log x - {x^4}] + c$
C
$\frac{1}{8}[{x^4}\log x - 4{x^2}] + c$
D
$\frac{1}{{16}}[4{x^4}\log x + {x^4}] + c$

✓

Answer

Correct option: B.

$\frac{1}{{16}}[4{x^4}\log x - {x^4}] + c$

(b) $I = \int {{x^3}\log x\,dx} $$ = \frac{{{x^4}}}{4}\log x - \int {\frac{{{x^4}}}{4}\frac{1}{x}dx + c} $
$ = \frac{{{x^4}}}{4}\log x - \int {\frac{{{x^3}}}{4}dx\, = \,\frac{{{x^4}}}{4}\log x - \frac{{{x^4}}}{{16}} + c} $
$ = \frac{1}{{16}}[4{x^4}\log x - {x^4}] + 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 "MCQ" from 7.1 inderfinite integral→7.1 inderfinite integral — all question types→ગણિત ધોરણ 12 સાયન્સ question papers→Gujarat Board ધોરણ 12 સાયન્સ question papers→Gujarat Board question paper generator→

Similar questions

$\int_{}^{} {\frac{{{e^{2x}} + 1}}{{{e^{2x}} - 1}}\;dx} $ =

Let $X$ be a binomially distributed random variable with mean $4$ and variance $\frac{4}{3}$. Then $54 P ( X \leq 2)$ is equal to.

${d \over {dx}}{\cos ^{ - 1}}\sqrt {{{1 + {x^2}} \over 2}} = $

વક્ર $y=\frac{1}{2} x^{4}-5 x^{3}+18 x^{2}-19 x$ ને ............ બિંદુએ મહત્તમ ઢાળ મળે છે.

નિશ્રાયક $\left| {\,\begin{array}{*{20}{c}}1&3&5&1\\2&3&4&2\\8&0&1&1\\0&2&1&1\end{array}\,} \right|$ માં ઘટક $'4'$ નો સહઅવયવ મેળવો.

A bag contains $4$ red and $6$ black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are re turned to the bag. Ifnow a ball is drawn at random from the bag, then the probability that this drawn ball is red, is :

જો ${I_1} = \int_0^1 {{2^{{x^2}}}dx,\;} {I_2} = \int_0^1 {{2^{{x^3}}}dx} ,\;{I_3} = \int_1^2 {{2^{{x^2}}}dx} $,${I_4} = \int_1^2 {{2^{{x^3}}}dx} $, તો

જો $y = A\cos nx + B\sin nx,$ તો ${{{d^2}y} \over {d{x^2}}} = $

એકમ સદિશો $ \ \overrightarrow a \ $ અને $ \ \overrightarrow b \ $ માટે જો $ \ \overrightarrow a + 2\overrightarrow b \ $અને$5\overrightarrow a - 4\overrightarrow b \ $ એકબીજાનેલંબહોય,તો$\left(\overrightarrow{a}\overrightarrow{b}\right)=\ .......$

જો $I_{m, n}=\int_{0}^{1} x^{m-1}(1-x)^{n-1} d x, m, n \geq 1$ અને $\int_{0}^{1} \frac{x^{m-1}+x^{n-1}}{(1+x)^{m+n}} d x=\alpha I_{m, n}, \alpha \in R,$ તો $\alpha=..... .$