Download App

Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
$\int \frac{e^x}{x+1}[1+(x+1) \log (x+1)] d x$ equals
  • A
    $\frac{e^x}{x+1}+c$
  • B
    $e^x \frac{x}{x+1}+c$
  • C
    $e^x \log (x+1)+e^x+c$
  • ✓
    $e^x \log (x+1)+c$
✓

Answer

Correct option: D.
$e^x \log (x+1)+c$
 Let $I=\int \frac{e^x}{x+1}[1+(x+1) \log (x+1)] d x$
$=\int e^x\left[\frac{1}{x+1}+\log (x+1)\right] d x$
It is of the form $\int e^x\left[f(x)+f^{\prime}(x) d x\right]$,
where $f(x)=\log (x+1)$ and $f^{\prime}(x)=\frac{1}{x+1}$
So, $I=e^x \log (x+1)+C$

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 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

$\int\limits^{2\text{a}}_0\text{f}(\text{x})\text{dx}$ is equal to:
→
Let $f\,(x)\, = \,\left\{ {\begin{array}{*{20}{c}}
{ - 1\,,\,\,\,\, - 2\, \le x\, < \,0}\\
{{x^2} - 1,\,\,\,0,\, \le \,x\, \le 2}
\end{array}} \right.$ and $g\,(x)\, = \,\left| {f\,(x)\,} \right|\, + \,f\,(\,\left| x \right|\,),$ Then, in the interval $(-2\,,2),\,g$ is
→
If $x^2 + y^2 + sin\, y = 4$, then the value of $\frac{{{d^2}y}}{{d{x^2}}}$ at the point $(- 2, 0)$ is
→
$\int_0^\pi \frac{1}{1+\sin x} dx$ equals
→
For which of the following values of $m$, the area of the region bounded by the curve $y = x - {x^2}$ and the line $y = mx$ equals $\frac{9}{2}$
→
If $\text{f}(\text{x})=\sqrt{\text{x}^2+6\text{x}+9},$ then f'(x) is equal to:
→
Choose the correct answer from the given four options:
At $\text{x}=\frac{5\pi}{6},\text{ f(x)}=2\sin3\text{x}+3\cos\text{x}$ is 6:
→
If the direction ratios of two lines are given by $3lm - 4ln + mn = 0$ and $l + 2m + 3n = 0,$ then the angle between the lines is:
→
Let a function $f:[0,5] \rightarrow \mathrm{R}$ be continuous. $f(1)=3$ and $\mathrm{F}$ be defined as

$\mathrm{F}(\mathrm{x})=\int\limits_{1}^{\mathrm{x}} \mathrm{t}^{2} \mathrm{g}(\mathrm{t}) \mathrm{dt},$ where $\mathrm{g}(\mathrm{t})=\int\limits_{1}^{\mathrm{t}} \mathrm{f}(\mathrm{u}) \mathrm{du}$

Then for the function $\mathrm{F}$, the point $\mathrm{x}=1$ is 

→
If the vectors $6i - 2j + 3k,\,\,2i + 3j - 6k$ and $3i + 6j - 2k$ form a triangle, then it is
→