What is the integral from-infinity to infinity of 1/(e^x+e^{-x)} ?

The integral from-infinity to infinity of 1/(e^x+e^{-x)} is pi/2

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integral from-infinity to infinity of 1/(e^x+e^{-x)}

\int_{- \infty}^{\infty} \frac{1}{e ^{x} + e ^{- x}} d x

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

\int_{- \infty}^{\infty} \frac{1}{e ^{x} + e ^{- x}} d x

Compute the indefinite integral:

\int \frac{1}{e ^{x} + e ^{- x}} d x = arctan (e^{x}) + C

Compute the boundaries:

\int_{- \infty}^{\infty} \frac{1}{e ^{x} + e ^{- x}} d x = \frac{π}{2} - 0

= \frac{π}{2} - 0

Simplify

= \frac{π}{2}

f (x) = x^{13}

\frac{d}{d x} (\frac{x ^{3} + x - 1}{2})

x \to 2 lim (10)

y^{^{''}} - \frac{3}{x} y^{^{'}} - \frac{7}{x ^{2}} y = 0

t - 2 + e^{- 5 t} - sin (5 t) + 1.5

What is the integral from-infinity to infinity of 1/(e^x+e^{-x)} ?
The integral from-infinity to infinity of 1/(e^x+e^{-x)} is pi/2