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Problem ∫ 1 − cos x cos α − cos x d x \int \sqrt{\frac{1 - \cos x}{\cos \alpha - \cos x}}\,dx ∫ c o s α − c o s x 1 − c o s x d x 0 < α < x < π 0 < \alpha < x < \pi 0 < α < x < π 2 ln ( cos α 2 − cos x 2 ) + c 2\ln\left(\cos \frac{\alpha}{2} - \cos \frac{x}{2}\right) + c 2 ln ( cos 2 α − cos 2 x ) + c 2 ln ( cos α 2 − cos x 2 ) + c \sqrt{2}\ln\left(\cos \frac{\alpha}{2} - \cos \frac{x}{2}\right) + c 2 ln ( cos 2 α − cos 2 x ) + c 2 2 ln ( cos α 2 − cos x 2 ) + c 2\sqrt{2}\ln\left(\cos \frac{\alpha}{2} - \cos \frac{x}{2}\right) + c 2 2 ln ( cos 2 α − cos 2 x ) + c − 2 sin − 1 ( cos x 2 cos α 2 ) + c -2\sin^{-1}\left(\frac{\cos \frac{x}{2}}{\cos \frac{\alpha}{2}}\right) + c − 2 sin − 1 ( c o s 2 α c o s 2 x ) + c Browse the problem library