What is laplacetransform 5t^2-2e^t ?

The answer to laplacetransform 5t^2-2e^t is (10)/(s^3)-2/(s-1)

laplacetransform 5t^2-2e^t

laplace transform

5 t^{2} - 2 e^{t}

\frac{10}{s ^{3}} - \frac{2}{s - 1}

Solution steps

L {5 t^{2} - 2 e^{t}}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= 5 L {t^{2}} - 2 L {e^{t}}

L {t^{2}} : \frac{2}{s ^{3}}

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

= 5 \cdot \frac{2}{s ^{3}} - 2 \cdot \frac{1}{s - 1}

Refine

5 \frac{2}{s ^{3}} - 2 \frac{1}{s - 1} : \frac{10}{s ^{3}} - \frac{2}{s - 1}

= \frac{10}{s ^{3}} - \frac{2}{s - 1}

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

d er i v a t i v e x^{3} - 8 x^{2} + 19 x - 12

\int_{5}^{10} (3 x + 3) d x

\int \frac{1}{t ^{3} + t ^{2} - 2 t} d t

\int \frac{32 x ^{2}}{( x - 15 ) ( x + 5 ) ^{2}} d x

What is laplacetransform 5t^2-2e^t ?
The answer to laplacetransform 5t^2-2e^t is (10)/(s^3)-2/(s-1)