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From: Vladimir Bondarenko on 3 Aug 2010 21:15
Hello,

Mathematica:

Integrate[Erf[ArcSin[z]]/Sqrt[1 + z], {z, 0, 1}]

Maple:

int(erf(arcsin(z))/sqrt(1 + z), z= 0..1);

?
Cheers,

Vladimir Bondarenko

Co-founder, CEO, Mathematical Director

http://www.cybertester.com/ Cyber Tester Ltd.

----------------------------------------------------------------

"We must understand that technologies
like these are the way of the future."

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http://groups.google.com/group/sci.math/msg/9f429c3ea5649df5

"...... the challenges imply that a solution is built within the
framework of the existent CAS functions & built-in definitions."

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From: Valeri Astanoff on 4 Aug 2010 04:30
On 4 août, 03:15, Vladimir Bondarenko <v...(a)cybertester.com> wrote:
> Hello,
>
> Mathematica:
>
> Integrate[Erf[ArcSin[z]]/Sqrt[1 + z], {z, 0, 1}]
>
> Maple:
>
> int(erf(arcsin(z))/sqrt(1 + z), z= 0..1);
>
>                  ?
> Cheers,
>
> Vladimir Bondarenko
>
> Co-founder, CEO, Mathematical Director
>
> http://www.cybertester.com/ Cyber Tester Ltd.
>
> ----------------------------------------------------------------
>
> "We must understand that technologies
> like these are the way of the future."
>
> ----------------------------------------------------------------
>
> http://groups.google.com/group/sci.math/msg/9f429c3ea5649df5
>
> "...... the challenges imply that a solution is built within the
> framework of the existent CAS functions & built-in definitions."
>
> ----------------------------------------------------------------
> ----------------------------------------------------------------

Good day,

A partly manual solution with mma 6 :

In[1]:= f[z_] = Erf[ArcSin[z]]/Sqrt[1 + z];

In[2]:= g[t_] = f[z] dz /. z -> Sin[t] /. dz -> Cos[t] //
Simplify[#, 0 < t < \[Pi]/2] &

Out[2]= (Cos[t]*Erf[t])/Sqrt[1 + Sin[t]]


In[3]:= Integrate[g[t], {t, 0, \[Pi]/2}]

Out[3]= 2*Sqrt[2]*Erf[Pi/2] + ((1 + I)*(-1 + Erfc[I/4 + Pi/2] -
(1 - I)*Erfi[1/4] + Erfi[1/4 + (I*Pi)/2]))/E^(1/16)


In[4]:= % // N // Chop

Out[4]= 0.40731

Numerical check:

In[5]:= NIntegrate[f[z], {z, 0, 1}]

Out[5]= 0.40731

--
v.a.
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