What is the integral of e^{-t}cos(pi)t ?

The integral of e^{-t}cos(pi)t is e^{-t}t+e^{-t}+C

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integral of e^{-t}cos(pi)t

\int e^{- t} cos (π) t d t

e^{- t} t + e^{- t} + C

Solution steps

\int e^{- t} cos (π) t d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= cos (π) \cdot \int e^{- t} t d t

cos (π) = - 1

= (- 1) \cdot \int e^{- t} t d t

Apply Integration By Parts

: - e^{- t} t - \int - e^{- t} d t

= (- 1) (- e^{- t} t - \int - e^{- t} d t)

\int - e^{- t} d t = e^{- t}

= (- 1) (- e^{- t} t - e^{- t})

Simplify

= e^{- t} t + e^{- t}

Add a constant to the solution

= e^{- t} t + e^{- t} + C

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What is the integral of e^{-t}cos(pi)t ?
The integral of e^{-t}cos(pi)t is e^{-t}t+e^{-t}+C