Integrate with respect to x- e2xe2x-2-

The correct option is D ln(e^2x 2)2+C Consider the given integral. #10; #10; #160; #10;I=∫e^2Xe^2X 2dx #10; #10; #160; #10;t=e^2X 2 ...

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Standard XII

Mathematics

Integration by Substitution

Integrate wit...

Question

Integrate with respect to x:
$\frac{e^{2 x}}{e^{2 x} - 2}$ .

l n (e^{2 x} - 2) + C

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l n (e^{2 x} + 2) + C

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\frac{l n (e^{2 x} - 2)}{2} + C

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l n (e^{x} - 2) + C

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Solution

The correct option is D $\frac{l n (e^{2 x} - 2)}{2} + C$
Consider the given integral.

$I = \int \frac{e^{2 X}}{e^{2 X} - 2} d x$

$t = e^{2 X} - 2$

$d x = \frac{d t}{2 e^{2 X}}$

$= \frac{1}{2} \int \frac{1}{t} d t$

$= \frac{1}{2} ln (t) + C$

$= \frac{1}{2} ln (e^{2 X} - 2) + C$

Hence, this is the required result

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Similar questions

Match the statements of Column I with values of Column II
$\begin{matrix} C o l u m n I & C o l u m n I I (A) \int \frac{e^{2 x} - 2 e^{x}}{e^{2 x} + 1} d x = A l n (e^{2 x} + 1) + B t a n^{- 1} (e^{x}) + c & (p) A = - \frac{1}{2}, B = - \frac{1}{4} (B) \int \sqrt{x + \sqrt{x^{2} + 2}} d x = A {x + \sqrt{x^{2} + 2}}^{\frac{3}{2}} + \frac{B}{\sqrt{x + \sqrt{x^{2} + 2}}} + c & (q) A = \frac{1}{2}, B = - 2 (C) \int \frac{c o s 8 x - c o s 7 x}{1 + 2 c o s 5 x} d x = A s i n 3 x + B s i n 2 x + c & (r) A = \frac{1}{3}, B = - 2 (D) \int \frac{l n x}{x^{3}} d x = A \frac{l n x}{x^{2}} + \frac{B}{x^{2}} + c & (s) A = \frac{1}{3}, B = - \frac{1}{2} \end{matrix}$

Find the integral of the given function w.r.t - x

$y = e^{2 x} + \frac{1}{x^{2}}$

Q. Integrate

\frac{d x}{[1 - e^{2 x}]^{(} 1 / 2)}

Q. Integrate:

\int e^{2 x - 3} + 7^{4 - 3 \frac{x}{2}} + sin (3 x - \frac{1}{2}) + cos (\frac{2}{5} x - 2) d x

Q. The integral

\int \frac{e^{3 {log}_{e} 2 x} + 5 e^{2 {log}_{e} 2 x}}{e^{4 {log}_{e} x} + 5 e^{3 {log}_{e} x} - 7 e^{2 {log}_{e} x}} d x, x > 0,

is equal to :
(where c is a constant of integration)

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Integrate with respect to x:e2xe2x−2.

The correct option is D ln(e2x−2)2+CConsider the given integral. I=∫e2Xe2X−2dx t=e2X−2 dx=dt2e2X =12∫1tdt =12ln(t)+C =12ln(e2X−2)+C Hence, this is the required result

Integrate with respect to x:
$\frac{e^{2 x}}{e^{2 x} - 2}$ .