Optimal. Leaf size=15 \[ \frac {x^2 \log (x)}{\sqrt {c x^4}} \]
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Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {1, 15, 29}
\begin {gather*} \frac {x^2 \log (x)}{\sqrt {c x^4}} \end {gather*}
Antiderivative was successfully verified.
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Rule 1
Rule 15
Rule 29
Rubi steps
\begin {align*} \int \frac {x}{\sqrt {2+2 a-2 (1+a)+c x^4}} \, dx &=\int \frac {x}{\sqrt {c x^4}} \, dx\\ &=\frac {x^2 \int \frac {1}{x} \, dx}{\sqrt {c x^4}}\\ &=\frac {x^2 \log (x)}{\sqrt {c x^4}}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} \frac {x^2 \log (x)}{\sqrt {c x^4}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 14, normalized size = 0.93
method | result | size |
default | \(\frac {x^{2} \ln \left (x \right )}{\sqrt {c \,x^{4}}}\) | \(14\) |
risch | \(\frac {x^{2} \ln \left (x \right )}{\sqrt {c \,x^{4}}}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 13, normalized size = 0.87 \begin {gather*} \frac {x^{2} \log \left (x\right )}{\sqrt {c x^{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 16, normalized size = 1.07 \begin {gather*} \frac {\sqrt {c x^{4}} \log \left (x\right )}{c x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x}{\sqrt {c x^{4}}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 4.58, size = 14, normalized size = 0.93 \begin {gather*} \frac {\log \left (x^{2} \sqrt {{\left | c \right |}}\right )}{2 \, \sqrt {c}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.07 \begin {gather*} \int \frac {x}{\sqrt {c\,x^4}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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