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(-Log[Cos[((b + c)*x)/2] - Sin[((b + c)*x)/2]] + Log[Cos[((b + c)*x)/2] + Sin[((b + c)*x)/2]])/(b + c)


Integrate[Sec[b*x + c*x], x] ==
(-Log[Cos[((b + c)*x)/2] - Sin[((b + c)*x)/2]] + Log[Cos[((b + c)*x)/2] + Sin[((b + c)*x)/2]])/ (b + c)



Integrate[Sec[b x + c x], x] == 

          (b + c) x        (b + c) x
(-Log[Cos[---------] - Sin[---------]] + 
              2                2
 
            (b + c) x        (b + c) x
    Log[Cos[---------] + Sin[---------]]) / (b + c)
                2                2

Time to compute: 0.04 second

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