_ ^ dx e^ - 2x ( e^ 2x + 1) ^2 =

MCQ

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

✓
$\frac{{ - 1}}{{2({e^{2x}} + 1)}} + c$
B
$\frac{1}{{2({e^{2x}} + 1)}} + c$
C
$\frac{1}{{{e^{2x}} + 1}} + c$
D
$\frac{{ - 1}}{{{e^{2x}} + 1}} + c$

✓

Answer

Correct option: A.

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

a
(a)$\int_{}^{} {\frac{{dx}}{{{e^{ - 2x}}{{({e^{2x}} + 1)}^2}}}} = \int_{}^{} {\frac{{{e^{2x}}dx}}{{{{({e^{2x}} + 1)}^2}}}} $
Put $t = {e^{2x}} + 1 \Rightarrow \frac{{dt}}{2} = {e^{2x}}dx,$ then it reduces to
$\frac{1}{2}\int_{}^{} {\frac{1}{{{t^2}}}} \,dt = - \frac{1}{{2t}} + c = \frac{{ - 1}}{{2({e^{2x}} + 1)}} + c.$

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

Choose the correct answer from the given four options.If $\text{P}(\text{A}\cap\text{B})=\frac{7}{10},$ and $\text{P}(\text{B})=\frac{17}{20},$ then $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)$ equas:

→

$\int_{}^{} {\frac{{{x^3} - 1}}{{{x^3} + x}}dx = } $

→

If the function $f : R \rightarrow A$ given by $\text{f(x)}=\frac{\text{x}^2}{\text{x}^2+1}$ is a surjection, then $ A =$

→

Let $\mathrm{f}:[0,3] \rightarrow \mathrm{R}$ be defined by

$f(x)=\min \{x-[x], 1+[x]-x\}$

where $[\mathrm{x}]$ is the greatest integer less than or equal to $\mathrm{x}$. Let $\mathrm{P}$ denote the set containing all $x \in[0,3]$ where $f$ is discontinuous, and $Q$ denote the set containing all $x \in(0,3)$ where $f$ is not differentiable. Then the sum of number of elements in $\mathrm{P}$ and $\mathrm{Q}$ is equal to $......$

→

Area bounded by the curvey $\text{y}=\text{x}+\sin\text{x}$ and its inverse function between the ordinates $\text{x}=0$ and $\text{x}=2\pi$ is:

→

Let $x, y$ be two variables and $x > 0, xy = 1,$ then minimum value of $x + y$ is :

→

$\int\limits_{\frac{\pi }{4}}^{\frac{\pi }{4}} {{{\log }_e}\left( {\sin x + \cos x} \right)\,dx}$ is equal to

→

If the lines $\frac{x-k}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x+1}{3}=\frac{y+2}{2}=\frac{z+3}{1}$ are co-planar, then the value of $k$ is $.....$

→

If $f(x) = \frac{{2x - 1}}{{x + 5}}$$(x \ne - 5)$, then ${f^{ - 1}}(x)$ is equal to

→

A solution of the equation ${\tan ^{ - 1}}(1 + x)$ $ + {\tan ^{ - 1}}(1 - x)$ $ = \frac{\pi }{2}$ is