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

so:

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

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

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