_ ^ 1 [ (x - 1) ^3 (x + 2) ^5 ] ^ 1/4 ;dx = - Vidyadip

MCQ

$\int_{}^{} {\frac{1}{{{{[{{(x - 1)}^3}{{(x + 2)}^5}]}^{1/4}}}}\;dx} $=

✓
$\frac{4}{3}{\left( {\frac{{x - 1}}{{x + 2}}} \right)^{1/4}} + c$
B
$\frac{4}{3}{\left( {\frac{{x + 2}}{{x - 1}}} \right)^{1/4}} + c$
C
$\frac{1}{3}{\left( {\frac{{x - 1}}{{x + 2}}} \right)^{1/4}} + c$
D
$\frac{1}{3}{\left( {\frac{{x + 2}}{{x - 1}}} \right)^{1/4}} + c$

✓

Answer

Correct option: A.

$\frac{4}{3}{\left( {\frac{{x - 1}}{{x + 2}}} \right)^{1/4}} + c$

(a)$\int_{}^{} {\frac{1}{{{{[{{(x - 1)}^3}{{(x + 2)}^5}]}^{1/4}}}}} \,dx = \int_{}^{} {\frac{1}{{{{\left( {\frac{{x - 1}}{{x + 2}}} \right)}^{3/4}}{{(x + 2)}^2}}}} \,dx$
$ = \frac{1}{3}\int_{}^{} {\frac{1}{{{t^{3/4}}}}\,dt} $, $\left\{ {\because \,\,\,\frac{{x - 1}}{{x + 2}} = t \Rightarrow \frac{3}{{{{(x + 2)}^2}}}\,dx = dt} \right\}$
$ = \frac{1}{3}\left( {\frac{{{t^{1/4}}}}{{1/4}}} \right) + c = \frac{4}{3}{t^{1/4}} + c = \frac{4}{3}{\left( {\frac{{x - 1}}{{x + 2}}} \right)^{1/4}} + 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

In a simultaneous toss of four coins, what is the probability of getting exactly three heads

જો $2\hat a = \hat b \times \hat c + 2\hat b$ હોય તો $\left| {2\hat a + \hat b + \hat c} \right|$ ની બધી શક્ય કિમતોનો સરવાળો મેળવો.

જો $\vec a = \hat i + \hat j + \hat k,\,\,\vec b = \hat i - \hat j + \hat k,\,\,\vec c = \hat i + 2\hat j + \hat k$ , હોય તો $\left| {\begin{array}{*{20}{c}}
{\vec a.\vec a}&{\vec a.\vec b}&{\vec a.\vec c} \\
{\vec b.\vec a}&{\vec b.\vec b}&{\vec b.\vec c} \\
{\vec c.\vec a}&{\vec c.\vec b}&{\vec c.\vec c}
\end{array}} \right|$ ની કિમત મેળવો.

ધારોકે $f$ એ $\left[0, \frac{\pi}{2}\right]$ પર વ્યાખ્યાયિત એવું વિકલનીય વિધેય છે,કે જેથી $f(x) > 0$ અને $f(x)+\int \limits_0^x f(t) \sqrt{1-\left(\log _e f(t)\right)^2} d t=e, \forall x \in\left[0, \frac{\pi}{2}\right]$ Then $\left(6 \log _{ e } f \left(\frac{\pi}{6}\right)\right)^2=............$

જો $y = {\sin ^{ - 1}}\sqrt {1 - {x^2}} $, તો $dy/dx = $

જો $\omega = - \frac{1}{2} + i\frac{{\sqrt 3 }}{2}$. તો $\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{ - 1 - {\omega ^2}}&{{\omega ^2}}\\1&{{\omega ^2}}&{{\omega ^4}}\end{array}\,} \right|= . . . $

જો $\int_{}^{} {\sin 5x\cos 3x\;dx = - \frac{{\cos 8x}}{{16}}} + A$, તો $A = $

The value of the integral $\int\limits_4^{10} {\frac{{\left[ {{x^2}} \right]dx}}{{\left[ {{x^2} - 28x + 196} \right] + \left[ {{x^2}} \right]}}}$ મેળવો. [ કે જ્યાં $\left[ x \right]$ મહતમ પૃણાંક છે .]

જા $\begin{bmatrix} 2 & 3 & 4\end{bmatrix} \begin{bmatrix} 1 & x & 3 \\ 2 & 4 & 5 \\ 3 & 2 & x\end{bmatrix} \begin{bmatrix} x \\ 2 \\ 0\end{bmatrix} =0$ હોય તો $x=.........$

$\overrightarrow a,\overrightarrow b,\overrightarrow c$ એકમ સદિશો છે , $\overrightarrow b$ અને $\overrightarrow c$ સમાંત૨ સદિશો નથી. જો $\overrightarrow a\times \left(\overrightarrow b\times \overrightarrow c\right)=\frac{\overrightarrow b+ \overrightarrow c}{\sqrt2}$ હોય , તો $\left(\overrightarrow a,^{\wedge} \overrightarrow b\right)=\ ...........$