1. ## Improper integrals:

$\int_{\frac{1}{2}}^{2} \frac{dz}{z(ln{z})^{\frac{1}{5}}}$

so:

$\lim{t\to{1^{-}}} \int_{\frac{1}{2}}^{t} {\frac{dz}{z(ln{z})^{\frac{1}{5}}} + \lim{t\to{1^{+}}}\int_{t}^{2}\frac{dz}{z(ln{z})^{\ frac{1}{5}}}$

$\lim{t\to 1^{-}} \frac{5}{4} (ln{z})^{\frac{4}{5}}\big|_{\frac{1}{2}}^{t} + \lim{t\to 1^{+}} \frac{5}{4} (ln{z})^{\frac{4}{5}}$

when i evaluate this.... the answer doesnt appear to be the sam as the back of book:
Answer at back of book : 0]

Edit:
kindly delete this thread for double posting its because of lagging

2. When I evaluated the integral in Mathematica 6 I got an imaginary solution so if the book was looking for real solutions you might have mistaken a null set (zero with a line through it) for a zero. Below is the answer mathematica gave me.. Hope this helps

1.6866 -0.548011 ä

3. Originally Posted by jandrewross
When I evaluated the integral in Mathematica 6 I got an imaginary solution so if the book was looking for real solutions you might have mistaken a null set (zero with a line through it) for a zero. Below is the answer mathematica gave me.. Hope this helps

1.6866 -0.548011 ä

I should mention that he is taking z to be a real variable here, not a complex one, as you can see by the limits so the value of the integral must be real.

-Dan