Integrating by parts?
1. The problem statement, all variables and given/known data
[tex]\text {Evaluate } \int^m_1 x^{3}ln{x}\,dx[/tex] 2. Relevant equations 3. The attempt at a solution Integrating by parts, but not sure which term to substitute out...it's not turning out clean...argh I've done every other problem except for this one, can someone just provide the first step? Much appreciated. 
Re: Integrating by parts?
I don't know what you mean by "I'm not sure which term to substitute out?" What is the method for integration by parts: you should have a formula, no? What specifically are you confused with, with respect to this formula?

Re: Integrating by parts?
You should try substituting for v and du, the terms for which vdu is easy to integrate. It's harder to integrate ln than it is to differentiate it, so that provides an obvious choice.

Re: Integrating by parts?
Since you have x^{3}ln x dx, and want u(x) dv, there are really just two choices: either u(x)= x^{3} and dv= ln(x)dx or u(x)= ln(x) and dv= x^{3}dv. Try both and see which gives you a decent integral!

Re: Integrating by parts?
Thanks, I integrated it successfully, but since this is a definite integral, at the end I'm not quite sure what to do with the boundaries, namely with the m term. Is it okay to leave the answer as an expression of both m and x?
It comes out to this: [tex]\frac {1}{4} (x^{4} ln{x}  \int^m_1 x^{3} \,dx) [/tex] 
Hi avr10! :smile:
Quote:
[tex]\left[\frac {1}{4} x^{4} ln{x} \right]^m_1 [/tex] :smile: 
Re: Integrating by parts?
Hm? Why is that?

Re: Integrating by parts?
Because that's what the little numbers at top and bottom of the integral sign mean!
[tex]\int_a^b f(x)dx= F(b) F(a)[/tex] where F is an antiderivative of f. The result of a definite integral is a number, not a function of x. 
Re: Integrating by parts?
Integrating by parts using the standard formula gives me
[tex]\left[ln(x)*\frac {1}{3} x^{3} \frac {1}{9}x^{3}\right]^m_1 [/tex] Following up by the formula presented by HallsofIvy, I get: [tex]ln(m)\frac{3}{9}*m^{3}\frac{1}{9}*m^{3}+\frac{1}{9}[/tex] Which is pulled together to: [tex]ln(m)+\frac {1}{9}\frac {4}{9}m^3[/tex] Voila? Edit: HallsofIvy, in this case the answer is not a number, but yes, it is a constant. 
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