已知：
r(t)=A*cos(b*t)*exp(a*t)+B*sin(b*t)*exp(a*t) 0<t<=t1时
r(t1)-A*cos(b*(t-t1))*exp(a*(t-t1))+B*sin(b*(t-t1))*exp(a*(t-t1)) t>t1时

求：
r(t)的积分函数R(t)
其中：a b A B 都是常数量

[此贴子已经被作者于2007-6-21 10:42:03编辑过]

int(A*cos(b*t)*exp(a*t)+B*sin(b*t)*exp(a*t),t)

rt1=subs(r,t,t1)-A*cos(b*(t-t1))*exp(a*(t-t1))+B*sin(b*(t-t1))*exp(a*(t-t1))

rt1 =

A*cos(b*t1)*exp(a*t1)+B*sin(b*t1)*exp(a*t1)-A*cos(b*(t-t1))*exp(a*(t-t1))+B*sin(b*(t-t1))*exp(a*(t-t1))

?int(rt1,t)

ans =

A*cos(b*t1)*exp(a*t1)*t+B*sin(b*t1)*exp(a*t1)*t-A*(a/(a^2+b^2)*exp(a*t-a*t1)*cos(-b*t+b*t1)-b/(a^2+b^2)*exp(a*t-a*t1)*sin(-b*t+b*t1))+B*(-b/(a^2+b^2)*exp(a*t-a*t1)*cos(-b*t+b*t1)-a/(a^2+b^2)*exp(a*t-a*t1)*sin(-b*t+b*t1))

?

谢谢