laplacetransform 2t^2e^t

解答

拉普拉斯变换

2 t^{2} e^{t}

\frac{4}{( s - 1 ) ^{3}}

求解步骤

L {2 e^{t} t^{2}}

利用拉普拉斯变换的常数乘法特性:

对于函数

f (t)

和常数

a : L {a \cdot f (t)} = a \cdot L {f (t)}

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

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

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

整理

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

= \frac{4}{( s - 1 ) ^{3}}

\frac{d ^{3}}{d x ^{3}} (e^{x^{2}})

\int \frac{x}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

\frac{\partial}{\partial y} (\frac{x}{x ^{2} + y ^{2}})

\int_{1200}^{1210} 0.1 x d x

x \to 0 lim (x^{3} \cdot ln (x))