Optimal. Leaf size=12 \[ \log \left (e+\left (-2 x+x^2\right )^2\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 16, normalized size of antiderivative = 1.33, number of steps used = 1, number of rules used = 1, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {1587} \begin {gather*} \log \left (x^4-4 x^3+4 x^2+e\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1587
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (e+4 x^2-4 x^3+x^4\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 12, normalized size = 1.00 \begin {gather*} \log \left (e+(-2+x)^2 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 17, normalized size = 1.42 \begin {gather*} \log \left (x^{4} - 4 \, x^{3} + 4 \, x^{2} + e\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 18, normalized size = 1.50
method | result | size |
derivativedivides | \(\ln \left ({\mathrm e}+x^{4}-4 x^{3}+4 x^{2}\right )\) | \(18\) |
default | \(\ln \left ({\mathrm e}+x^{4}-4 x^{3}+4 x^{2}\right )\) | \(18\) |
norman | \(\ln \left ({\mathrm e}+x^{4}-4 x^{3}+4 x^{2}\right )\) | \(18\) |
risch | \(\ln \left ({\mathrm e}+x^{4}-4 x^{3}+4 x^{2}\right )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 17, normalized size = 1.42 \begin {gather*} \log \left (x^{4} - 4 \, x^{3} + 4 \, x^{2} + e\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 17, normalized size = 1.42 \begin {gather*} \ln \left (x^4-4\,x^3+4\,x^2+\mathrm {e}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 17, normalized size = 1.42 \begin {gather*} \log {\left (x^{4} - 4 x^{3} + 4 x^{2} + e \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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