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## moment of inertia of a rectangular prism

I was trying to derive the formula for the moment of inertia of a rectangular prism at its centre of mass. And ended up with this:

$$\frac{1}{2}M(a/2)^{2}+2\frac{M}{ab}\int^{b/2}_{a/2}arccos(\frac{a^{2}}{2r^{2}}-1)rdr+4\frac{M}{ab}\int^{\sqrt{a^{2}+b^{2}}}_{b/2}(\frac{\pi}{2}-arccos\frac{b/2}{r}-arccos\frac{a/2}{r})rdr$$

Due to the limitation of my knowledge in Calculus, I was stuck here. Can anyone help me solve these two integral:

$$\int arccos(\frac{a^{2}}{2r^{2}}-1)rdr$$

$$\int (\frac{\pi}{2}-arccos\frac{b/2}{r}-arccos\frac{a/2}{r})rdr$$

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