How to evaulate $\int \cos x \sqrt{5 + \cos^2 x} dx$?

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How do I evaluate $$ \int \cos x \sqrt{5 + \cos^2 x} dx? $$

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HINT:

$$\int\cos x\sqrt{5+\cos^2x}dx=\int\cos x\sqrt{6-\sin^2x}dx$$

Now put $\sin x=u$ and use Point $\#8$ of this or this