Question

Can you explain to me how to go about integrating a product of three functions ?

For example: Integrate (e^x)(ln(x))(sinx)dx

Answer 1

i am not sure that is the best example because i think you can just write it as \(\mathcal{Im} \int ~ e^x \ln(x) e^{ix} ~dx \)

but if you take the product rule: \((u v w)' = u' v w + u v' w + uv w'\)

perhaps you can then use \(\int u' v w ~ dx= uvw - \int u v' w ~ dx - \int uv w' ~ dx\)

but without actually trying it out, i think you'd need to luck out and have two of the functions that are easy to differentiate/integrate, .....

Answer 2

@freckles

Answer 3

How did you get that formula with the integral?

Answer 4

which one?

Answer 5

uvw one