inverselaplace 1/((s-5)^3)

解答

的拉普拉斯逆变换

\frac{1}{( s - 5 ) ^{3}}

\frac{e ^{5 t} t ^{2}}{2}

求解步骤

L^{- 1} {\frac{1}{( s - 5 ) ^{3}}}

应用逆变换法则: if

L^{- 1} {F (s)} = f (t)

则

L^{- 1} {F (s - a)} = e^{a t} f (t)

对于

\frac{1}{( s - 5 ) ^{3}} : a = 5, F (s) = \frac{1}{s ^{3}}

= e^{5 t} L^{- 1} {\frac{1}{s ^{3}}}

L^{- 1} {\frac{1}{s ^{3}}} : \frac{t ^{2}}{2}

= \frac{e ^{5 t} t ^{2}}{2}

\frac{\partial}{\partial x} (56 e^{8 x} y)

\int_{0}^{\frac{π}{2}} (sin (2 x)) d x

x \to 1 - lim (2 x^{3} + 5 x)

\int_{- 2}^{5} (- 2) d x

x \to 7 lim (f (x))