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Question Number 100829 by M±th+et+s last updated on 28/Jun/20

h e l l o e v e r y o n e

p r o v e t h a t

\int_{0}^{\frac{π}{2}} {c o s}^{u} (x) c o s (a x) a r c t a n (b c o s (x)) d x

= \frac{2^{- u - 2} . π . b . Γ (u + 2)}{Γ (\frac{u - a + 3}{2}) Γ (\frac{u + a + 3}{2})} . x_{4} F_{3} (\begin{matrix} \frac{1}{2}, 1 + \frac{u}{2}, \frac{u + 3}{2}, - b^{2} \\ \frac{3}{2}, \frac{u - a + 3}{2}, \frac{u + a + 3}{2} \end{matrix})

R e u > - 1, ∣ a r g (1 + b^{2}) ∣< π