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Category: Integration

hello-every-one-prove-that-0-pi-2-cos-u-x-cos-ax-arctan-b-cos-x-dx-2-u-2-pi-b-u-2-u-a-3-2-u-a-3-2-x-4-F-3-1-2-1-u-2-u-3-2-b-2-3-2-u-a-3-2-

Question Number 100829 by  M±th+et+s last updated on 28/Jun/20 helloeveryoneprovethat0π2cosu(x)cos(ax)arctan(bcos(x))dx$$=\frac{\mathrm{2}^{−{u}−\mathrm{2}} .\pi.{b}.\Gamma\left({u}+\mathrm{2}\right)}{\Gamma\left(\frac{{u}−{a}+\mathrm{3}}{\mathrm{2}}\right)\Gamma\left(\frac{{u}+{a}+\mathrm{3}}{\mathrm{2}}\right)}.{x}_{\mathrm{4}} {F}_{\mathrm{3}} (12,1+u2,u+32,b232,ua+32,u+a+32)