Integrate Expression: Help & Tips

[Black Armadillo]

I'm trying to integrate the following expression:
$$\int\frac{E_0*sin(\omega*t)}{L}*e^{\frac{R}{L}t}dt$$

Any hints on what method to use? I'd like to figure out how to do this integral by hand so please don't just give me the answer. I've already used my calculator to get that. Thanks for the help.

 

[slider142]

Assuming E₀, L, and R are constants, you can use the product rule: if u and v are functions of x, then (u(x)v(x))' = u'(x)v(x) + u(x)v'(x) which means
$$\int u'(x)v(x) dx = u(x)v(x) - \int u(x)v'(x) dx$$
This is also known as integration by parts. From inspection, it appears you will have to apply it twice and then solve for the integral algebraically.

 

[dx]

Write sin(ωt) as Im(e^iωt).