Optimal. Leaf size=22 \[ \frac {\log \left (a^3+\sqrt {-a} x\right )}{\sqrt {-a}} \]
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Rubi [A] time = 0.00, antiderivative size = 22, 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 = {31} \begin {gather*} \frac {\log \left (a^3+\sqrt {-a} x\right )}{\sqrt {-a}} \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rubi steps
\begin {align*} \int \frac {1}{a^3+\sqrt {-a} x} \, dx &=\frac {\log \left (a^3+\sqrt {-a} x\right )}{\sqrt {-a}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 22, normalized size = 1.00 \begin {gather*} \frac {\log \left (a^3+\sqrt {-a} x\right )}{\sqrt {-a}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{a^3+\sqrt {-a} x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.84, size = 23, normalized size = 1.05 \begin {gather*} -\frac {\sqrt {-a} \log \left (-\sqrt {-a} a^{2} + x\right )}{a} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.09, size = 19, normalized size = 0.86 \begin {gather*} \frac {\log \left ({\left | a^{3} + \sqrt {-a} x \right |}\right )}{\sqrt {-a}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 19, normalized size = 0.86 \begin {gather*} \frac {\ln \left (a^{3}+\sqrt {-a}\, x \right )}{\sqrt {-a}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 18, normalized size = 0.82 \begin {gather*} \frac {\log \left (a^{3} + \sqrt {-a} x\right )}{\sqrt {-a}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 16, normalized size = 0.73 \begin {gather*} \frac {\ln \left (x-{\left (-a\right )}^{5/2}\right )}{\sqrt {-a}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 19, normalized size = 0.86 \begin {gather*} \frac {\log {\left (a^{3} + x \sqrt {- a} \right )}}{\sqrt {- a}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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