What is laplacetransform sin(5pit) ?

The answer to laplacetransform sin(5pit) is (5pi)/(s^2+25pi^2)

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laplacetransform sin(5pit)

laplace transform

sin (5 π t)

\frac{5 π}{s ^{2} + 25 π ^{2}}

Solution steps

L {sin (5 π t)}

Use Laplace Transform table:

L {sin (a t)} = \frac{a}{s ^{2} + a ^{2}}

L {sin (5 π t)} = \frac{5 π}{s ^{2} + ( 5 π ) ^{2}}

= \frac{5 π}{s ^{2} + ( 5 π ) ^{2}}

= \frac{5 π}{s ^{2} + 25 π ^{2}}

\int \frac{7 x ^{2} + 9 x + 7}{( x ^{2} + 1 ) ^{2}} d x

\int_{4}^{5} \frac{x}{x ^{2} + 4 x + 20} d x

\int (- 5 csc^{2} (x)) d x

x cos (2 x), 1

x \to + 1 lim (e^{4 x^{3} - 4 x})

What is laplacetransform sin(5pit) ?
The answer to laplacetransform sin(5pit) is (5pi)/(s^2+25pi^2)