laplacetransform 2(t-3)^2+15(t-3)+26

解答

拉普拉斯变换

2 (t - 3)^{2} + 15 (t - 3) + 26

\frac{4}{s ^{3}} + \frac{3}{s ^{2}} - \frac{1}{s}

求解步骤

L {2 (t - 3)^{2} + 15 (t - 3) + 26}

展开

2 (t - 3)^{2} + 15 (t - 3) + 26 : 2 t^{2} + 3 t - 1

= L {2 t^{2} + 3 t - 1}

利用拉普拉斯变换的线性特性:

对于函数

f (t), g (t)

和常数

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

= 2 L {t^{2}} + 3 L {t} - L {1}

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

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

L {1} : \frac{1}{s}

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

整理

2 \frac{2}{s ^{3}} + 3 \frac{1}{s ^{2}} - \frac{1}{s} : \frac{4}{s ^{3}} + \frac{3}{s ^{2}} - \frac{1}{s}

= \frac{4}{s ^{3}} + \frac{3}{s ^{2}} - \frac{1}{s}

\frac{d}{d x} (\frac{8 ( 4 ^{x} )}{x ^{4}})

\int_{0}^{\frac{1}{3}} \frac{5}{1 + 9 x ^{2}} d x

\frac{d}{d x} (\frac{1}{2} ln (\frac{x}{2}))

\frac{d}{d x} (x^{\frac{2}{3}} (x - 4))

\frac{d}{d x} ((2 x - 8)^{5})