SOLUTION: How do i solve the integral of sin(60t)e^(20t)

Question 25734: How do i solve the integral of sin(60t)e^(20t)
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
LET US USE THE SYMBOL
I[F(X)DX]FOR INTEGRAL F(X)W.R.T.X
LET K=I[SIN(60T)*E^20T DT]....INTEGRATING BY PARTS...I[UV]=U*I[V]-I[U'I[V]]
=SIN(60T)*I[E^20T DT]-I[60COS(60T)*I[E^20T DT]DT]
=SIN(60T)(E^20T)/20-I[3COS(60T)*E^20T DT]
=SIN(60T)(E^20T)/20-[3COS(60T)*I[E^20T DT]-I[(-180SIN(60T))*I[E^20T DT]DT]
=SIN(60T)(E^20T)/20-[3COS(60T)*I[E^20T DT]-I[(-180SIN(60T))*I[E^20T DT]DT]
=SIN(60T)(E^20T)/20-[3COS(60T)*E^20T/20-I[-9SIN(60T)*E^20T DT]]
=SIN(60T)(E^20T)/20-[3COS(60T)*E^20T/20+9K]
K=SIN(60T)(E^20T)/20-3COS(60T)*E^20T/20-9K
10K=SIN(60T)(E^20T)/20-3COS(60T)*E^20T/20
K=(1/200)*{SIN(60T)(E^20T)-3COS(60T)*E^20T}
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