Optimal. Leaf size=46 \[ \frac {x^{1-m} \, _2F_1\left (1,\frac {1-m}{3};\frac {4-m}{3};-\frac {x^3}{a^3}\right )}{a^3 (1-m)} \]
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Rubi [A] time = 0.01, antiderivative size = 46, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {364} \[ \frac {x^{1-m} \text {Hypergeometric2F1}\left (1,\frac {1-m}{3},\frac {4-m}{3},-\frac {x^3}{a^3}\right )}{a^3 (1-m)} \]
Antiderivative was successfully verified.
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Rule 364
Rubi steps
\begin {align*} \int \frac {x^{-m}}{a^3+x^3} \, dx &=\frac {x^{1-m} \, _2F_1\left (1,\frac {1-m}{3};\frac {4-m}{3};-\frac {x^3}{a^3}\right )}{a^3 (1-m)}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 45, normalized size = 0.98 \[ -\frac {x^{1-m} \, _2F_1\left (1,\frac {1}{3}-\frac {m}{3};\frac {4}{3}-\frac {m}{3};-\frac {x^3}{a^3}\right )}{a^3 (m-1)} \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {x^{-m}}{a^3+x^3} \, dx \]
Verification is Not applicable to the result.
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fricas [F] time = 1.03, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{{\left (a^{3} + x^{3}\right )} x^{m}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (a^{3} + x^{3}\right )} x^{m}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.03, size = 0, normalized size = 0.00 \[\int \frac {x^{-m}}{a^{3}+x^{3}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (a^{3} + x^{3}\right )} x^{m}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.02 \[ \int \frac {1}{x^m\,\left (a^3+x^3\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [C] time = 2.97, size = 92, normalized size = 2.00 \[ - \frac {m x x^{- m} \Phi \left (\frac {x^{3} e^{i \pi }}{a^{3}}, 1, \frac {1}{3} - \frac {m}{3}\right ) \Gamma \left (\frac {1}{3} - \frac {m}{3}\right )}{9 a^{3} \Gamma \left (\frac {4}{3} - \frac {m}{3}\right )} + \frac {x x^{- m} \Phi \left (\frac {x^{3} e^{i \pi }}{a^{3}}, 1, \frac {1}{3} - \frac {m}{3}\right ) \Gamma \left (\frac {1}{3} - \frac {m}{3}\right )}{9 a^{3} \Gamma \left (\frac {4}{3} - \frac {m}{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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