Optimal. Leaf size=15 \[ x^2 \left (-\frac {2205 (-8+x)}{x}+\log (3)\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {6}
\begin {gather*} 17640 x-x^2 (2205-\log (3)) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int (17640+x (-4410+2 \log (3))) \, dx\\ &=17640 x-x^2 (2205-\log (3))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} 17640 x-2205 x^2+x^2 \log (3) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 16, normalized size = 1.07
method | result | size |
gosper | \(x \left (x \ln \left (3\right )-2205 x +17640\right )\) | \(12\) |
norman | \(\left (\ln \left (3\right )-2205\right ) x^{2}+17640 x\) | \(13\) |
default | \(x^{2} \ln \left (3\right )-2205 x^{2}+17640 x\) | \(16\) |
risch | \(x^{2} \ln \left (3\right )-2205 x^{2}+17640 x\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 15, normalized size = 1.00 \begin {gather*} x^{2} \log \left (3\right ) - 2205 \, x^{2} + 17640 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 15, normalized size = 1.00 \begin {gather*} x^{2} \log \left (3\right ) - 2205 \, x^{2} + 17640 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 10, normalized size = 0.67 \begin {gather*} x^{2} \left (-2205 + \log {\left (3 \right )}\right ) + 17640 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 15, normalized size = 1.00 \begin {gather*} x^{2} \log \left (3\right ) - 2205 \, x^{2} + 17640 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 12, normalized size = 0.80 \begin {gather*} \left (\ln \left (3\right )-2205\right )\,x^2+17640\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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