The Divergence of a Polar Vector Function

[transmini]

Homework Statement

Find the divergence of the function $\vec{v} = (rcos\theta)\hat{r}+(rsin\theta)\hat{\theta}+(rsin\theta cos\phi)\hat{\phi}$

Homework Equations

$\nabla\cdot\vec{v}=\frac{1}{r^2}\frac{\partial}{\partial r}(r^2v_r)+\frac{1}{r sin\theta}\frac{\partial}{\partial \theta}(sin\theta v_\theta) + \frac{1}{r sin\theta} \frac{\partial v_\phi}{\partial\phi}$

The Attempt at a Solution

$\nabla\cdot\vec{v}=\frac{1}{r^2}\frac{\partial}{\partial r}(r^3 cos\theta)+\frac{1}{r sin\theta}\frac{\partial}{\partial \theta}(rsin^2\theta) + \frac{1}{r sin\theta} \frac{\partial}{\partial\phi}(rsin\theta cos\phi)$
$\nabla\cdot\vec{v}=\frac{1}{r^2}(3r^2cos\theta)+\frac{1}{r sin\theta}(2rsin\theta cos\theta) + \frac{1}{r sin\theta} (-rsin\theta sin\phi)$
$\nabla\cdot\vec{v}=3cos\theta+2cos\theta-sin\phi$
$\nabla\cdot\vec{v}=5cos\theta-sin\phi$

Except, the answer shouldn't have the second term in it at all and should just be $5cos\theta$ (I don't know 100% certain what the answer is, just the wolfram alpha gives $5cos\theta$ and that the Divergence Theorem doesn't hold with the second term and would hold if that term were gone like in wolfram's answer)

Where did I make a mistake here? Thanks in advance

Edit: Okay I spoke too soon on the Divergence Theorem not holding, as it appears to hold now that I double checked that problem's work. So is there just a problem with wolfram's answer?

 

[Orodruin]

Can you provide a link to exactly what you put into Wolfram Alpha?