laplacetransform tsin(3t)+2tcos(t)

解答

拉普拉斯变换

t sin (3 t) + 2 t cos (t)

\frac{6 s}{( s ^{2} + 9 ) ^{2}} - \frac{2 ( - s ^{2} + 1 )}{( s ^{2} + 1 ) ^{2}}

求解步骤

L {t sin (3 t) + 2 t cos (t)}

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)}

= L {t sin (3 t)} + 2 L {t cos (t)}

L {t sin (3 t)} : \frac{6 s}{( s ^{2} + 9 ) ^{2}}

L {t cos (t)} : - \frac{- s ^{2} + 1}{( s ^{2} + 1 ) ^{2}}

= \frac{6 s}{( s ^{2} + 9 ) ^{2}} + 2 (- \frac{- s ^{2} + 1}{( s ^{2} + 1 ) ^{2}})

整理

\frac{6 s}{( s ^{2} + 9 ) ^{2}} + 2 (- \frac{- s ^{2} + 1}{( s ^{2} + 1 ) ^{2}}) : \frac{6 s}{( s ^{2} + 9 ) ^{2}} - \frac{2 ( - s ^{2} + 1 )}{( s ^{2} + 1 ) ^{2}}

= \frac{6 s}{( s ^{2} + 9 ) ^{2}} - \frac{2 ( - s ^{2} + 1 )}{( s ^{2} + 1 ) ^{2}}

t an g e n t f (x) = \frac{2 x + 1}{x + 2}, at x = 1

\frac{\partial}{\partial x} (- (5 x^{3} + 5 x y^{2}))

\frac{\partial}{\partial h} (x^{2} h)

ma c l a u r in \frac{1}{x + 2}

\int \frac{x ^{2} - 2}{x ^{2} + x} d x