laplacetransform cos(2t-2)e^{3t}

解答

拉普拉斯变换

cos (2 t - 2) e^{3 t}

\frac{cos ( 2 ) ( s - 3 ) + 2 sin ( 2 )}{( s - 3 ) ^{2} + 4}

求解步骤

L {e^{3 t} cos (2 t - 2)}

应用变换法则: if

L {f (t)} = F (s)

则

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

对于

cos (2 t - 2) e^{3 t} : f (t) = cos (2 t - 2), a = 3

= L {cos (2 t - 2)} (s - 3)

L {cos (2 t - 2)} : \frac{cos ( 2 ) s + 2 sin ( 2 )}{s ^{2} + 4}

= \frac{cos ( 2 ) ( s - 3 ) + 2 sin ( 2 )}{( s - 3 ) ^{2} + 4}

\int_{0}^{1.75} 1500 x d x

\int \frac{1}{x ^{3} - 4 x ^{2} + 8 x} d x

x \to 3 lim (\frac{1}{6 - 2 x})

\int \frac{3 x - 1}{x ^{2} - 3 x - 4} d x

\int e^{2 t + e^{t}} d t