What is t(e^{-st}cos(t))dt ?

The solution to t(e^{-st}cos(t))dt is (tcos(t)dt)/(e^{ts)}

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simplify t(e^{-st}cos(t))dt

simplify

t (e^{- s t} cos (t)) d t

\frac{t cos ( t ) d t}{e ^{t s}}

Solution steps

t (e^{- s t} cos (t)) d t

Apply exponent rule:

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

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

Multiply fractions:

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

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

Multiply:

1 \cdot t = t

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

\frac{1}{2} e^{- 2 l n (4)}

e^{- x^{2}} e^{- x^{2}}

2 (210)

What is t(e^{-st}cos(t))dt ?
The solution to t(e^{-st}cos(t))dt is (tcos(t)dt)/(e^{ts)}