∫dx1+e^2x #160; #160; = ∫ ( e^2x/1+e^2x+1)dx #160; #160; = ∫e^2x1+e^2xdx + ∫ 1.dx #160; = 1/2∫2e^2x/1+e^2xdx+x+c #160; = 1/2l ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Integration of Trigonometric Functions

-∫ dx 1+ e 2x

Question

$- \int \frac{d x}{1 + e^{2 x}}$

Open in App

Solution

$- \int \frac{d x}{1 + e^{2 x}}$
$= \int (- \frac{e^{2 x}}{1 + e^{2 x}} + 1) d x$
$= - \int \frac{e^{2 x}}{1 + e^{2 x}} d x + \int 1. d x$
$= - \frac{1}{2} \int \frac{2 e^{2 x}}{1 + e^{2 x}} d x + x + c$
$= \frac{- 1}{2} l n ∣ ∣ 1 + e^{2 x} ∣ ∣ + x + c$
$= - (\frac{- 1}{2} l n ∣ ∣ 1 + e^{2 x} ∣ ∣ + x) + c$
$\Rightarrow \frac{1}{2} ∣ ∣ 1 + e^{2 x} ∣ ∣ - x + c$

Suggest Corrections

Similar questions

\int \frac{d x}{\sqrt{1 - e^{2 x}}}

\int \frac{d x}{\sqrt{e^{2 x} - 1}}

\int \frac{d x}{\sqrt{1 - e^{2 x}}}

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

\int \frac{d x}{\sqrt{e^{2 x}} - 1}

Join BYJU'S Learning Program