Optimal. Leaf size=11 \[ \frac {1}{2} x \left (2+\log \left (x^2\right )\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 2295} \begin {gather*} \frac {1}{2} x \log \left (x^2\right )+x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2295
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (4+\log \left (x^2\right )\right ) \, dx\\ &=2 x+\frac {1}{2} \int \log \left (x^2\right ) \, dx\\ &=x+\frac {1}{2} x \log \left (x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} x+\frac {1}{2} x \log \left (x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 9, normalized size = 0.82 \begin {gather*} \frac {1}{2} \, x \log \left (x^{2}\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 9, normalized size = 0.82 \begin {gather*} \frac {1}{2} \, x \log \left (x^{2}\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 10, normalized size = 0.91
method | result | size |
default | \(x +\frac {x \ln \left (x^{2}\right )}{2}\) | \(10\) |
norman | \(x +\frac {x \ln \left (x^{2}\right )}{2}\) | \(10\) |
risch | \(x +\frac {x \ln \left (x^{2}\right )}{2}\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 9, normalized size = 0.82 \begin {gather*} \frac {1}{2} \, x \log \left (x^{2}\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.16, size = 9, normalized size = 0.82 \begin {gather*} \frac {x\,\left (\ln \left (x^2\right )+2\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 8, normalized size = 0.73 \begin {gather*} \frac {x \log {\left (x^{2} \right )}}{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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