The conversation between human and AI assistant.
How do I evaluate the integral [math]\int\log x\sin x\,dx[/math]?
I think I'll choose [math]\log x[/math] as [math]u[/math] and [math]\sin x\,dx[/math] as [math]dv[/math].
Good choice! Now we need to find the derivative of [math]\log x[/math] and the antiderivative of [math]\sin x[/math]. What are they?