Sam Blake schrieb:
Some of you may find this result interesting...
In[1047]:= $Version
Out[1047]= "13.2.0 for Mac OS X x86 (64-bit) (November 18, 2022)"
In[1048]:= Integrate[(2 - Sqrt[7] x^2 + 3 x^4)/(2 + Sqrt[7] x^2 - x^4)^2, x]
Out[1048]= 1/60 (30 x AppellF1[1/2, 2, 2, 3/2, (2 x^2)/(Sqrt[7] + Sqrt[15]), (2 x^2)/(Sqrt[7] - Sqrt[15])] -
5 Sqrt[7] x^3 AppellF1[3/2, 2, 2, 5/2, (2 x^2)/(Sqrt[7] + Sqrt[15]), (2 x^2)/(Sqrt[7] - Sqrt[15])] +
9 x^5 AppellF1[5/2, 2, 2, 7/2, (2 x^2)/(Sqrt[7] + Sqrt[15]), (2 x^2)/(Sqrt[7] - Sqrt[15])])
Acording to Derive 6.10, the antiderivative is simply:
INT((2 - SQRT(7)*x^2 + 3*x^4)/(2 + SQRT(7)*x^2 - x^4)^2, x)
- x/(x^4 - SQRT(7)*x^2 - 2)
Martin.
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