What is laplacetransform sqrt(t)+3t ?

The answer to laplacetransform sqrt(t)+3t is (sqrt(pi))/(2s^{3/2)}+3/(s^2)

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laplacetransform sqrt(t)+3t

laplace transform

t + 3 t

\frac{π}{2 s ^{\frac{3}{2}}} + \frac{3}{s ^{2}}

Solution steps

L {t + 3 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)}

= L {t} + 3 L {t}

L {t} : \frac{π}{2 s ^{\frac{3}{2}}}

L {t} : \frac{1}{s ^{2}}

= \frac{π}{2 s ^{\frac{3}{2}}} + 3 \cdot \frac{1}{s ^{2}}

Refine

\frac{π}{2 s ^{\frac{3}{2}}} + 3 \frac{1}{s ^{2}} : \frac{π}{2 s ^{\frac{3}{2}}} + \frac{3}{s ^{2}}

= \frac{π}{2 s ^{\frac{3}{2}}} + \frac{3}{s ^{2}}

n = 0 \sum \infty 2 (\frac{2}{3})^{3 n}

\int \frac{x}{x + 1 - ( x + 1 )} d x

\frac{\partial}{\partial y} (x^{2} e^{y z^{2}})

\int_{0}^{1} x 1 - x d x

\frac{3}{2 3 x + 13}, at x = - 3

What is laplacetransform sqrt(t)+3t ?
The answer to laplacetransform sqrt(t)+3t is (sqrt(pi))/(2s^{3/2)}+3/(s^2)