Optimal. Leaf size=21 \[ 7-x+\frac {x^2}{3}+25 x^2 \log ^2(x) \]
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Rubi [A] time = 0.02, antiderivative size = 20, normalized size of antiderivative = 0.95, number of steps used = 5, number of rules used = 3, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 2304, 2305} \begin {gather*} \frac {x^2}{3}+25 x^2 \log ^2(x)-x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2304
Rule 2305
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \left (-3+2 x+150 x \log (x)+150 x \log ^2(x)\right ) \, dx\\ &=-x+\frac {x^2}{3}+50 \int x \log (x) \, dx+50 \int x \log ^2(x) \, dx\\ &=-x-\frac {73 x^2}{6}+25 x^2 \log (x)+25 x^2 \log ^2(x)-50 \int x \log (x) \, dx\\ &=-x+\frac {x^2}{3}+25 x^2 \log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 20, normalized size = 0.95 \begin {gather*} -x+\frac {x^2}{3}+25 x^2 \log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 18, normalized size = 0.86 \begin {gather*} 25 \, x^{2} \log \relax (x)^{2} + \frac {1}{3} \, x^{2} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.08, size = 18, normalized size = 0.86 \begin {gather*} 25 \, x^{2} \log \relax (x)^{2} + \frac {1}{3} \, x^{2} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 19, normalized size = 0.90
method | result | size |
default | \(\frac {x^{2}}{3}-x +25 x^{2} \ln \relax (x )^{2}\) | \(19\) |
norman | \(\frac {x^{2}}{3}-x +25 x^{2} \ln \relax (x )^{2}\) | \(19\) |
risch | \(\frac {x^{2}}{3}-x +25 x^{2} \ln \relax (x )^{2}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 33, normalized size = 1.57 \begin {gather*} \frac {25}{2} \, {\left (2 \, \log \relax (x)^{2} - 2 \, \log \relax (x) + 1\right )} x^{2} + 25 \, x^{2} \log \relax (x) - \frac {73}{6} \, x^{2} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.20, size = 13, normalized size = 0.62 \begin {gather*} \frac {x\,\left (75\,x\,{\ln \relax (x)}^2+x-3\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 15, normalized size = 0.71 \begin {gather*} 25 x^{2} \log {\relax (x )}^{2} + \frac {x^{2}}{3} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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