What is the integral from 0 to infinity of e^{-x}cos(x) ?

The integral from 0 to infinity of e^{-x}cos(x) is 1/2

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integral from 0 to infinity of e^{-x}cos(x)

\int_{0}^{\infty} e^{- x} cos (x) d x

\frac{1}{2}

Decimal Notation

0.5

Solution steps

\int_{0}^{\infty} e^{- x} cos (x) d x

Compute the indefinite integral:

\int e^{- x} cos (x) d x = \frac{e ^{- x} sin ( x )}{2} - \frac{e ^{- x} cos ( x )}{2} + C

Compute the boundaries:

\int_{0}^{\infty} e^{- x} cos (x) d x = 0 - (- \frac{1}{2})

= 0 - (- \frac{1}{2})

Simplify

= \frac{1}{2}

\frac{\partial}{\partial x} (e^{- 2 t} cos (π x))

\frac{d y}{d t} = \frac{t}{y e ^{y + t^{2}}}

\frac{d}{d x} (sin^{4} (3 x) tan^{3} (4 x))

\int \frac{x ^{2}}{a ^{2} + ( x - b ) ^{2}} d x

\int 5 x cos (8 x) d x

What is the integral from 0 to infinity of e^{-x}cos(x) ?
The integral from 0 to infinity of e^{-x}cos(x) is 1/2