Optimal. Leaf size=26 \[ x+3 (3-x) \left (-3-\left (x+x^2\right )^2-\log \left (\frac {5}{4}\right )\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 31, normalized size of antiderivative = 1.19, number of steps
used = 1, number of rules used = 0, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} 3 x^5-3 x^4-15 x^3-9 x^2+x \left (10+3 \log \left (\frac {5}{4}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-9 x^2-15 x^3-3 x^4+3 x^5+x \left (10+3 \log \left (\frac {5}{4}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 31, normalized size = 1.19 \begin {gather*} 10 x-9 x^2-15 x^3-3 x^4+3 x^5+3 x \log \left (\frac {5}{4}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.22, size = 30, normalized size = 1.15
method | result | size |
gosper | \(-x \left (-3 x^{4}+3 x^{3}+15 x^{2}+3 \ln \left (\frac {4}{5}\right )+9 x -10\right )\) | \(28\) |
default | \(-3 \ln \left (\frac {4}{5}\right ) x +3 x^{5}-3 x^{4}-15 x^{3}-9 x^{2}+10 x\) | \(30\) |
norman | \(\left (3 \ln \left (5\right )-6 \ln \left (2\right )+10\right ) x -9 x^{2}-15 x^{3}-3 x^{4}+3 x^{5}\) | \(34\) |
risch | \(3 x^{5}-3 x^{4}-15 x^{3}-6 x \ln \left (2\right )+3 x \ln \left (5\right )-9 x^{2}+10 x\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 29, normalized size = 1.12 \begin {gather*} 3 \, x^{5} - 3 \, x^{4} - 15 \, x^{3} - 9 \, x^{2} - 3 \, x \log \left (\frac {4}{5}\right ) + 10 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 29, normalized size = 1.12 \begin {gather*} 3 \, x^{5} - 3 \, x^{4} - 15 \, x^{3} - 9 \, x^{2} - 3 \, x \log \left (\frac {4}{5}\right ) + 10 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 32, normalized size = 1.23 \begin {gather*} 3 x^{5} - 3 x^{4} - 15 x^{3} - 9 x^{2} + x \left (- 6 \log {\left (2 \right )} + 3 \log {\left (5 \right )} + 10\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 29, normalized size = 1.12 \begin {gather*} 3 \, x^{5} - 3 \, x^{4} - 15 \, x^{3} - 9 \, x^{2} - 3 \, x \log \left (\frac {4}{5}\right ) + 10 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 30, normalized size = 1.15 \begin {gather*} 3\,x^5-3\,x^4-15\,x^3-9\,x^2+\left (10-3\,\ln \left (\frac {4}{5}\right )\right )\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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