Martin Rubey <[EMAIL PROTECTED]> writes:

> In[1]:= Integrate[ArcCos[Sin[2*z]]*Cos[z], {z,0,4*Pi/3}]
> 
> Limit::ztest: Unable to decide whether numeric quantities 
>        -I/3 Pi   I Sqrt[3]    (-2 I)/3 Pi    I Sqrt[3]
>     {-E        - --------- - E            + -----------}
>                    I/3 Pi                    (2 I)/3 Pi
>                   E                         E
>      are equal to zero. Assuming they are.
> 
>                            Pi
> Out[1]= 1 - 2 Sqrt[2] - ---------
>                         4 Sqrt[3]
> 
> In[2]:= N[%]
> 
> Out[2]= -2.28188

I should have added: Mathematica returns 

Integrate[ArcCos[Sin[2*z]]*Cos[z], z]
                               2
Out[1]= -2 Cos[z] Sqrt[Cos[2 z] ] Sec[2 z] + ArcCos[Sin[2 z]] Sin[z]


Martin


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