Need help solving definite integral

[noob314]

I need help on this one


$$\int_0^{100} \sqrt{x}ln{x}dx$$


I've tried integrating it by parts and ended up with the equation

[(2/3)(x^3/2)(lnx) - (4/9)(x^3/2)] from 0 to 100

However, I can't plug it in because there's no value of ln(0). So, I'm at a loss right now. Any idea on where to go from here?

 

[Bohrok]

$$x^{\frac{3}{2}}\ln x = x^{\frac{1}{2}}(x\ln x)$$

$$Let ~u = \frac{1}{x}. ~~Then ~\lim_{x\rightarrow0}(x\ln x) = \lim_{u\rightarrow+\infty}\frac{\ln\frac{1}{u}}{u}$$

Or you might try xlnx = ln(x^x) and use the limit of x^x as x→0+

 

[lanedance]

i think the integral is not well defined and you should be considering

$$\stackrel{lim}{a \rightarrow 0} \int_a^{100} dx.\sqrt{x}.ln(x)$$

 

[noob314]

$$x^{\frac{3}{2}}\ln x = x^{\frac{1}{2}}(x\ln x)$$

$$Let ~u = \frac{1}{x}. ~~Then ~\lim_{x\rightarrow0}(x\ln x) = \lim_{u\rightarrow+\infty}\frac{\ln\frac{1}{u}}{u}$$

Or you might try xlnx = ln(x^x) and use the limit of x^x as x→0+

Thanks. That really helped.