Question

Trouble with integral. I really need some help here guys!
Details below!
Use Biot-Savart law to calculate the magnetic field in a single point over a finite line.

Answer 1

I have the physics part pretty much done, but i get stuck trying to integrate.
\[\large B = \oint_{L} \frac{ \mu_0 I \space dl \times \hat{r} }{ 4\pi r^2 }\]\[\large = \frac{ \mu_0 I }{ 4 \pi } \int\limits_{-L}^{L} \frac{ \hat{z} \times (-z \space \hat{z} + R \space \hat{R}) }{ (z^2+ R^2)^{3/2} }dz = \frac{ \mu_0 I }{ 4 \pi } \int\limits_{-L}^{L} \frac{ R \hat{\phi} }{ (z^2+ R^2)^{3/2} }dz\]\[\large = \frac{ \mu_0 I }{ 4 \pi } R \hat{\phi} \int\limits_{-L}^{L} u^{-3/2}dz \]\[\large u = z^2 + R^2 \rightarrow du = 2z \space dz\]That substitution isn't going to work(?), any ideas on how I continue?