How to integrate something that keeps on repeating

[dwilmer]

Homework Statement

What is integral of e^t (1+3sint)?
I tried integ by parts but its not working
Im familiar with the technique where you end up with two idental integrals on either side, then you add one side to the other, and divide by 2.
This isn't working though. Mainly because the RHS will never be same as term on LHS, because the 1 either cancels or else becomes a t, at the first integration or differentiation.

Please help.

Homework Equations

The Attempt at a Solution

 

[Borek]

You mean

$$e^t (1+3\sin(t))$$

or

$$e^{t (1+3\sin(t))}$$

not that I will know in either case, just it is not clear to me what the question is.

 

[HallsofIvy]

Homework Statement

What is integral of e^t (1+3sint)?
I tried integ by parts but its not working
Im familiar with the technique where you end up with two idental integrals on either side, then you add one side to the other, and divide by 2.
This isn't working though. Mainly because the RHS will never be same as term on LHS, because the 1 either cancels or else becomes a t, at the first integration or differentiation.

Please help.

I suspect you mean $\int e^t (1+ 3sin(t)dt$ because Borek's suggested $\int e^{t(1+ 3sin(t)}dt$, while plausible from what you wrote, is intractible.

First, split the integral up: $\int e^t dt+ 3\int e^t sin(t)dt$. The first is easy and the second can be done by the technique you mention. One integration by parts gives a term of $\int e^t cos(t)dt$ and a second gives [itex]\int e^t sin(t)[/tex] again.

Homework Equations

The Attempt at a Solution

 

[urduworld]

thanks Halls