What is the integral from 0 to infinity of e^{-y/x} ?

The integral from 0 to infinity of e^{-y/x} is x

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integral from 0 to infinity of e^{-y/x}

\int_{0}^{\infty} e^{- \frac{y}{x}} d y

x

Solution steps

\int_{0}^{\infty} e^{- \frac{y}{x}} d y

Compute the indefinite integral:

\int e^{- \frac{y}{x}} d y = - x e^{- \frac{y}{x}} + C

Compute the boundaries:

\int_{0}^{\infty} e^{- \frac{y}{x}} d y = 0 - (- x)

= 0 - (- x)

Simplify

= x

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What is the integral from 0 to infinity of e^{-y/x} ?
The integral from 0 to infinity of e^{-y/x} is x