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

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$\frac{{1 - 2i}}{{2 + i}} + \frac{{4 - i}}{{3 + 2i}} = $

If $A, B$ and $C$ are any three sets, then $A \times (B \cup C)$ is equal to

The roots of the equation $\left| {\,\begin{array}{*{20}{c}}0&x&{16}\\x&5&7\\0&9&x\end{array}\,} \right| = 0$ are

The mean and standard deviation of $50$ observations are $15$ and $2$ respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is $70$ . If the correct mean is $16$ , then the correct variance is equal to

The mean and $S.D.$ of the marks of $200$ candidates were found to be $40$ and $15$ respectively. Later, it was discovered that a score of $40$ was wrongly read as $50$. The correct mean and $S.D.$ respectively are...

The sum of two forces is $18\, N$ and resultant whose direction is at right angles to the smaller force is $12\,N.$ The magnitude of the two forces are

The sum of two non-zero numbers is $4$ . The minimum value of the sum of their reciprocals is

The number of $p$ oints which can be expressed in the form $(p_1/q_ 1 , p_2/q_2)$, ($p_i$ and $q_i$ $(i = 1,2)$ are co-primes) and lie on the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$ is

If $ABCD$ is a cyclic quadrilateral, then the value of $\cos A - \cos B + \cos C - \cos D = $

If $A \cap B = B$, then