What is e^{-at}*cos(wt)dt ?

The solution to e^{-at}*cos(wt)dt is (cos(tw)dt)/(e^{at)}

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simplify e^{-at}*cos(wt)dt

simplify

e^{- a t} \cdot cos (wt) d t

\frac{cos ( tw ) d t}{e ^{a t}}

Solution steps

e^{- a t} cos (wt) d t

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{a t}} cos (tw) d t

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot cos ( wt ) d t}{e ^{a t}}

Multiply:

1 \cdot cos (wt) = cos (wt)

= \frac{cos ( tw ) d t}{e ^{a t}}

0.1 \cdot 1 0^{- 1}

e^{- c o s (t)}

4 \cdot π \cdot (3)^{2} \cdot 4

8.55 \cdot 1 0^{- 2}

131300 \cdot 2.52 \cdot 1 0^{- 10}

What is e^{-at}*cos(wt)dt ?
The solution to e^{-at}*cos(wt)dt is (cos(tw)dt)/(e^{at)}