Question

integrate the equation is
$1 - e {}^{x \:} \div 1 + e {}^{x}$
​

Answer 1

Answer:

Mark as brainliest

Step-by-step explanation:

This is an old favorite of mine.

Define

I=∫+∞−∞e−x2dx

Then

I2=(∫+∞−∞e−x2dx)(∫+∞−∞e−y2dy)

I2=∫+∞−∞∫+∞−∞e−(x2+y2)dxdy

Now change to polar coordinates

I2=∫+2π0∫+∞0e−r2rdrdθ

The θ integral just gives 2π, while the r integral succumbs to the substitution u=r2

I2=2π∫+∞0e−udu/2=π

So

I=π−−√

and your integral is half this by symmetry