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**sillyme** Please help with the following integral calculation:

$\displaystyle \int\!\!\!\!\int\!\!\!\!\int_V e^{{(x^2+y^2+z^2)}^{\frac{3}{2}}}dxdydz$ where $\displaystyle V=\{(x,y,z)|x^2+y^2+z^2\leq1\}$

I tried switching to spherical coordinates:

$\displaystyle x=r\cos\varphi\sin\theta$

$\displaystyle y=r\sin\varphi\sin\theta$

$\displaystyle z=r\cos\theta$

$\displaystyle dV=r^2 \sin \theta dr d \theta d\varphi$

with $\displaystyle 0\leq r\leq1$ but I'm not sure about the range of $\displaystyle \varphi$ and $\displaystyle \theta$