integral of 1 / [5 + 4 cosx] with limits 0 to (pi/2)

integral of 1 / [5 + 4 cosx] with limits 0 to (pi/2)

if the denominator contains sinx  or cosx in the first degree,  the  method is to use the substitution,
t = tan(x/2) and change dx
you also have to express sin(x) and cos(x)  in terms of tan(x/2) , then use completion of squares if necessary to integrate. If there are limits it is better to change the limits

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