Optimal. Leaf size=12 \[ -\frac {1}{3 \sqrt {a} x^3} \]
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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}{3 \sqrt {a} x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 2
Rule 12
Rule 30
Rubi steps
\begin {align*} \int \frac {1}{x^4 \sqrt {a+(2+2 c-2 (1+c)) x^4}} \, dx &=\int \frac {1}{\sqrt {a} x^4} \, dx\\ &=\frac {\int \frac {1}{x^4} \, dx}{\sqrt {a}}\\ &=-\frac {1}{3 \sqrt {a} x^3}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} -\frac {1}{3 \sqrt {a} x^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 9, normalized size = 0.75
method | result | size |
gosper | \(-\frac {1}{3 x^{3} \sqrt {a}}\) | \(9\) |
default | \(-\frac {1}{3 x^{3} \sqrt {a}}\) | \(9\) |
norman | \(-\frac {1}{3 x^{3} \sqrt {a}}\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 8, normalized size = 0.67 \begin {gather*} -\frac {1}{3 \, \sqrt {a} x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 8, normalized size = 0.67 \begin {gather*} -\frac {1}{3 \, \sqrt {a} x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 12, normalized size = 1.00 \begin {gather*} - \frac {1}{3 \sqrt {a} x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 4.50, size = 8, normalized size = 0.67 \begin {gather*} -\frac {1}{3 \, \sqrt {a} x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.33, size = 8, normalized size = 0.67 \begin {gather*} -\frac {1}{3\,\sqrt {a}\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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