Optimal. Leaf size=20 \[ 4 \left (-e^3+\frac {5}{2} x (3+x) (5+\log (x))\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.35, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {2313, 9} \begin {gather*} 55 x^2+10 \left (x^2+3 x\right ) \log (x)+180 x-5 (x+3)^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 9
Rule 2313
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=180 x+55 x^2+\int (30+20 x) \log (x) \, dx\\ &=180 x+55 x^2+10 \left (3 x+x^2\right ) \log (x)-\int 10 (3+x) \, dx\\ &=180 x+55 x^2-5 (3+x)^2+10 \left (3 x+x^2\right ) \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 1.05 \begin {gather*} 150 x+50 x^2+30 x \log (x)+10 x^2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 20, normalized size = 1.00 \begin {gather*} 50 \, x^{2} + 10 \, {\left (x^{2} + 3 \, x\right )} \log \relax (x) + 150 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.54, size = 21, normalized size = 1.05 \begin {gather*} 10 \, x^{2} \log \relax (x) + 50 \, x^{2} + 30 \, x \log \relax (x) + 150 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 22, normalized size = 1.10
method | result | size |
default | \(150 x +10 x^{2} \ln \relax (x )+50 x^{2}+30 x \ln \relax (x )\) | \(22\) |
norman | \(150 x +10 x^{2} \ln \relax (x )+50 x^{2}+30 x \ln \relax (x )\) | \(22\) |
risch | \(\left (10 x^{2}+30 x \right ) \ln \relax (x )+50 x^{2}+150 x\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 20, normalized size = 1.00 \begin {gather*} 50 \, x^{2} + 10 \, {\left (x^{2} + 3 \, x\right )} \log \relax (x) + 150 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.01, size = 10, normalized size = 0.50 \begin {gather*} 10\,x\,\left (\ln \relax (x)+5\right )\,\left (x+3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 19, normalized size = 0.95 \begin {gather*} 50 x^{2} + 150 x + \left (10 x^{2} + 30 x\right ) \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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