cost and constant how to integrate?

Question

integrate {[12/5(100+t)]cost}dt

what can i do vif it???
integration by part?
try alr bt fail

Answer 1

You get (12/5) [ Int 100 cos(t) dt + Int t cos(t) dt] = (12/5) [100 sin(t) + Int t cos(t) dt]

To integrate t cos(t), let's do it by parts, putting u = t and dv = cos(t) dt. Then,

Int t cos(t) dt = t sin(t) - Int sin(t) dt = t sin(t) + cos(t)

Therefore, your integral is (12/5) [100 sin(t) + t sin(t) + cos(t)] + C, where C is an integration constant.

Answer 2

You need to do integration by parts several times. Each time you take the trig part for dv. You will eventually get an equation for the integral. Along the way you will have to find the integral of e^(-st)sint dt, done similarly.

Answer 3

Integration by parts. I believe you're going to have to end up with 12/5(100sinx+xsinx+cosx)