# Homework Help: Repeating integration by parts

1. Feb 4, 2012

### cameuth

1. The problem statement, all variables and given/known data

integrate .5e^(t/50)*sin(t)

2. Relevant equations
integration by parts
uv-∫vdu

3. The attempt at a solution

I am currently in differential equations and I remember from cal II that I have to keep using the equation above until the integral loops around, then set it equal to something,... but I'm foggy on what it's equal to. Any help would be appreciated. thanks.

Last edited by a moderator: Feb 4, 2012
2. Feb 4, 2012

### vela

Staff Emeritus
Let's call the integral I. When you do integration by parts repeatedly, you eventually end up with

I = stuff + (something) I

At this point, you solve for I.

3. Feb 4, 2012

I believe that you should keep integrating by parts until you end up with something that looks like:

∫.5e^(t/50)*sin(t) = SOMETHING - ∫.5e^(t/50)*sin(t)

then you can add ∫.5e^(t/50)*sin(t) to both sides to get:

2*∫.5e^(t/50)*sin(t) = SOMETHING

so that

∫.5e^(t/50)*sin(t) = (1/2)*SOMETHING

EDIT: vela beat me to it

4. Feb 4, 2012

### cameuth

thanks. vela helped, and saladsamurai's elaboration was necessary. You guys are lifesavers.