How to evaluate this $\int_{0}^{\pi/2}(\cos x)^{a+b}\cos {(b-a)x}\, dx$

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Evaluate: $$\int_{0}^{\pi/2}(\cos x)^{a+b}\cos (b-a)x\, dx,0<a<1,a+b>1$$

This integral looks very simple, but I can't solve it. Any help is appreciated.