(x + 3) e^x (x + 4) ^2 , ,dx = , , - Vidyadip

MCQ

$\int {\frac{{(x + 3){e^x}}}{{{{(x + 4)}^2}}}\,\,dx = \,\,} $

A
$\frac{1}{{{{(x + 4)}^2}}} + c$
B
$\frac{{{e^x}}}{{{{(x + 4)}^2}}} + c$
✓
$\frac{{{e^x}}}{{x + 4}} + c$
D
$\frac{{{e^x}}}{{x + 3}} + c$

✓

Answer

Correct option: C.

$\frac{{{e^x}}}{{x + 4}} + c$

c
(c) $I = \int {\frac{{(x + 3){e^x}}}{{{{(x + 4)}^2}}}dx} $$I = \int {\frac{{1 + {{\tan }^2}x}}{{1 - {{\tan }^2}x}}dx} $
$ \Rightarrow I = \int {{e^x}\,\left( {\frac{1}{{x + 4}} - \frac{1}{{{{(x + 4)}^2}}}} \right)\,dx} $
$\therefore I = \frac{{{e^x}}}{{x + 4}} + c$.

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 "M.C.Q (1 Marks)" from 7.1 inderfinite integral→7.1 inderfinite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $A$, $B$ and $C$ are square matrices of order $3$ such that $A = \left[ {\begin{array}{*{20}{c}} x&0&1 \\ 0&y&0 \\ 0&0&z \end{array}} \right]$ and $\left| B \right| = 36$, $\left| C \right| = 4$, $\left( {x,y,z \in N} \right)$ and $\left| {ABC} \right| = 1152$ then the minimum value of $x + y + z$ is

If $\text{AB}=\text{A}$ and $\text{BA = B}$ then $\text{B}^2 $ is equal to:

$\text{B}$
$\text{A}$
$\text{-B}$
$\text{B}^2$

If the equation ${\sin ^{ - 1}}\sqrt x + {\cos ^{ - 1}}\sqrt {{x^2} - 1} + {\tan ^{ - 1}}\left( {\tan \,y} \right) = a$ has at least one solution, then number of integral values of $a$ is

If $\frac{{d[f(x)]}}{{dx}} = g(x)$ for $a \le x \le b,$ then $\int_a^b {f(x)\,\,g(x)\,dx} $ equals

If the function $f(x)=\left\{\begin{array}{cc}(1+|\cos x|) \frac{\lambda}{|\cos x|} & , 0 < x < \frac{\pi}{2} \\ \mu & , x=\frac{\pi}{2} \\ e^{\frac{\cot 6 x}{\cot 4 x }} & , \frac{\pi}{2} < x < \pi\end{array}\right.$ is continuous at $x =\frac{\pi}{2}$, then $9 \lambda+6 \log _{ e } \mu+\mu^6- e ^{6 \lambda}$ is equal to

A line passes through the points (6, −7, −1) and (2, −3, 1). The direction cosines of the line so directed that the angle made by it with the positive direction of x-axis is acute, is?

The equation of the curve passing through the origin and satisfying the differential equation $\left( {1 + {x^2}} \right)\,\frac{{dy}}{{dx}} + 2xy = 4{x^2}$ is

Let $f:\left( { - 1,1} \right) \to R$ be differentiable function with $f\left( 0 \right) = - 1$ and $f'\left( 0 \right) = 1$ . Let $g\left( x \right) = {\left[ {f\left( {2f\left( x \right) + 2} \right)} \right]^2}$ .Then $g'\left( 0 \right) = $

$\mathop \smallint \limits_0^1 \frac{{8{\rm{log}}\left( {1 + x} \right)}}{{1 + {x^2}}}dx = $

Let $f:[0,1] \rightarrow R$ (the set of all real numbers) be a function. Suppose the function $f$ is twice differentiable, $f(0)=f(1)=0$ and satisfies $f^{\prime \prime}(x)-2 f^{\prime}(x)+f(x) \geq e^x, x \in[0,1]$

$1.$ Which of the following is true for $0 < x < 1$ ?

$(A)$ $0 < $ f(x) $ < \infty$

$(B)$ $-\frac{1}{2} < f(x) < \frac{1}{2}$

$(C)$ $-\frac{1}{4} < f(x) < 1$

$(D)$ $-\infty < $ f $($ x $) < 0$

$2.$ If the function $e^{-x} f(x)$ assumes its minimum in the interval $[0,1]$ at $x=\frac{1}{4}$, which of the following is true?

$(A)$ $f^{\prime}(x)$

$(B)$ $f^{\prime}(x)>f(x), 0$

$(C)$ f $^{\prime}(x)$

$(D)$ $f^{\prime}(x)$

Give the answer question $1$ and $2.$