Question

How do you integrate e^2xsinxdx using integration by parts? I'll include the equation

Answer 1

\[\int\limits e^(2x)sinx dx\]

Answer 2

That's supposed to be e^2x where 2x is the power

Answer 3

int (u dv) = uv - int(v du)

Answer 4

I know the equation but how do you apply it? Whenever you integrate it goes back and forth with sinx and cosx. The answer ends up being \[\frac{ 1 }{ 5 }e^(2x)(2sinx-cosx)+C\] I just don't know where the 1/5 comes from