Optimal. Leaf size=12 \[ -\frac {1}{2 \sqrt {a} x^2} \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2, 12, 30} \begin {gather*} -\frac {1}{2 \sqrt {a} x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2
Rule 12
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{x^3 \sqrt {a+(2+2 c-2 (1+c)) x^4}} \, dx &=\int \frac {1}{\sqrt {a} x^3} \, dx\\ &=\frac {\int \frac {1}{x^3} \, dx}{\sqrt {a}}\\ &=-\frac {1}{2 \sqrt {a} x^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} -\frac {1}{2 \sqrt {a} x^2} \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}{x^3 \sqrt {a+(2+2 c-2 (1+c)) x^4}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.85, size = 8, normalized size = 0.67 \begin {gather*} -\frac {1}{2 \, \sqrt {a} x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 8, normalized size = 0.67 \begin {gather*} -\frac {1}{2 \, \sqrt {a} x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 9, normalized size = 0.75 \begin {gather*} -\frac {1}{2 \sqrt {a}\, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.04, size = 8, normalized size = 0.67 \begin {gather*} -\frac {1}{2 \, \sqrt {a} x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.40, size = 8, normalized size = 0.67 \begin {gather*} -\frac {1}{2\,\sqrt {a}\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 12, normalized size = 1.00 \begin {gather*} - \frac {1}{2 \sqrt {a} x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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