The discussion revolves around the integral ∫cosx(lnsinx)dx, focusing on the application of integration by parts and the choice of substitution for the variable u.
Participants are exploring different approaches to the problem, with some affirming the correctness of the original poster's method. There is a recognition of the complexity involved in using u-substitution followed by integration by parts, indicating a productive exchange of ideas.
There is some confusion regarding the appropriate choice of u for integration by parts, as well as the implications of using u-substitution in this context. The original poster's teacher's suggestion is also under consideration.
jdawg said:Homework Statement
∫cosx(lnsinx)dx
Homework Equations
The Attempt at a Solution
u=lnsinx dv=cosxdx
du=cosx/sinx dx v=sinx
=(lnsinx)(sinx)-∫(sinx)(cosx/sinx)dx
=(lnsinx)(sinx)-(sinx)+C
I thought that I did this correctly, but my teacher said that u should equal sinx. Why would u not equal lnsinx?
jackarms said:If you differentiate, you get the original function, so you did it correctly. I think your teacher was saying u should equal sinx if you're doing a simple u-sub to integrate, since that method works as well. You couldn't have u be sinx for an integration by parts, since it isn't a complete term in the integrand -- it's only part of the natural log.
jdawg said:Ohh ok! I didn't know you could use u substitution on that one. Thanks for clearing that up :)