Optimal. Leaf size=26 \[ 4+\frac {4-x^2+\frac {1}{4} x^5 \log ^2\left (x^2\right )}{x} \]
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Rubi [A]
time = 0.03, antiderivative size = 22, normalized size of antiderivative = 0.85, number of steps
used = 7, number of rules used = 3, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {14, 2341, 2342}
\begin {gather*} \frac {1}{4} x^4 \log ^2\left (x^2\right )-x+\frac {4}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2341
Rule 2342
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-4-x^2}{x^2}+x^3 \log \left (x^2\right )+x^3 \log ^2\left (x^2\right )\right ) \, dx\\ &=\int \frac {-4-x^2}{x^2} \, dx+\int x^3 \log \left (x^2\right ) \, dx+\int x^3 \log ^2\left (x^2\right ) \, dx\\ &=-\frac {x^4}{8}+\frac {1}{4} x^4 \log \left (x^2\right )+\frac {1}{4} x^4 \log ^2\left (x^2\right )+\int \left (-1-\frac {4}{x^2}\right ) \, dx-\int x^3 \log \left (x^2\right ) \, dx\\ &=\frac {4}{x}-x+\frac {1}{4} x^4 \log ^2\left (x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 22, normalized size = 0.85 \begin {gather*} \frac {4}{x}-x+\frac {1}{4} x^4 \log ^2\left (x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 21, normalized size = 0.81
method | result | size |
default | \(\frac {x^{4} \ln \left (x^{2}\right )^{2}}{4}+\frac {4}{x}-x\) | \(21\) |
norman | \(\frac {\frac {x^{5} \ln \left (x^{2}\right )^{2}}{4}-x^{2}+4}{x}\) | \(23\) |
risch | \(\frac {x^{4} \ln \left (x^{2}\right )^{2}}{4}-\frac {x^{2}-4}{x}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 20, normalized size = 0.77 \begin {gather*} \frac {1}{4} \, x^{4} \log \left (x^{2}\right )^{2} - x + \frac {4}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 22, normalized size = 0.85 \begin {gather*} \frac {x^{5} \log \left (x^{2}\right )^{2} - 4 \, x^{2} + 16}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 15, normalized size = 0.58 \begin {gather*} \frac {x^{4} \log {\left (x^{2} \right )}^{2}}{4} - x + \frac {4}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 20, normalized size = 0.77 \begin {gather*} \frac {1}{4} \, x^{4} \log \left (x^{2}\right )^{2} - x + \frac {4}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.30, size = 20, normalized size = 0.77 \begin {gather*} \frac {4}{x}-x+\frac {x^4\,{\ln \left (x^2\right )}^2}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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