What is laplacetransform e^tt ?

The answer to laplacetransform e^tt is 1/((s-1)^2)

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laplacetransform e^tt

laplace transform

e^{t} t

\frac{1}{( s - 1 ) ^{2}}

Solution steps

L {e^{t} t}

Use Laplace Transform table:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

For

e^{t} t : f (t) = e^{t}, k = 1

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

L {e^{t}} : \frac{1}{s - 1}

\frac{d}{d s} (\frac{1}{s - 1}) = - \frac{1}{( s - 1 ) ^{2}}

= (- 1)^{1} (- \frac{1}{( s - 1 ) ^{2}})

= \frac{1}{( s - 1 ) ^{2}}

\int \frac{1 - cos ( x )}{csc ^{2} ( x )} d x

\frac{d}{d x} ((8 x + 3)^{2})

\frac{d}{d x} ((3 x^{4} + 1)^{3})

\int sec^{2} (x) tan (x) d x

\frac{d}{d x} (\frac{C ^{2} - x ^{2}}{2 x})

What is laplacetransform e^tt ?
The answer to laplacetransform e^tt is 1/((s-1)^2)