Optimal. Leaf size=22 \[ 11+\log (5)-\log (x)-(4+x-x (x+\log (x)))^2 \]
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Rubi [B] time = 0.07, antiderivative size = 51, normalized size of antiderivative = 2.32, number of steps used = 11, number of rules used = 5, integrand size = 47, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.106, Rules used = {14, 2356, 2295, 2304, 2305} \begin {gather*} -x^4+2 x^3-2 x^3 \log (x)+7 x^2-x^2 \log ^2(x)+2 x^2 \log (x)-8 x+8 x \log (x)-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2295
Rule 2304
Rule 2305
Rule 2356
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-1+16 x^2+4 x^3-4 x^4}{x}-2 (1+x) (-4+3 x) \log (x)-2 x \log ^2(x)\right ) \, dx\\ &=-(2 \int (1+x) (-4+3 x) \log (x) \, dx)-2 \int x \log ^2(x) \, dx+\int \frac {-1+16 x^2+4 x^3-4 x^4}{x} \, dx\\ &=-x^2 \log ^2(x)+2 \int x \log (x) \, dx-2 \int \left (-4 \log (x)-x \log (x)+3 x^2 \log (x)\right ) \, dx+\int \left (-\frac {1}{x}+16 x+4 x^2-4 x^3\right ) \, dx\\ &=\frac {15 x^2}{2}+\frac {4 x^3}{3}-x^4-\log (x)+x^2 \log (x)-x^2 \log ^2(x)+2 \int x \log (x) \, dx-6 \int x^2 \log (x) \, dx+8 \int \log (x) \, dx\\ &=-8 x+7 x^2+2 x^3-x^4-\log (x)+8 x \log (x)+2 x^2 \log (x)-2 x^3 \log (x)-x^2 \log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.01, size = 51, normalized size = 2.32 \begin {gather*} -8 x+7 x^2+2 x^3-x^4-\log (x)+8 x \log (x)+2 x^2 \log (x)-2 x^3 \log (x)-x^2 \log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.60, size = 47, normalized size = 2.14 \begin {gather*} -x^{4} - x^{2} \log \relax (x)^{2} + 2 \, x^{3} + 7 \, x^{2} - {\left (2 \, x^{3} - 2 \, x^{2} - 8 \, x + 1\right )} \log \relax (x) - 8 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.16, size = 48, normalized size = 2.18 \begin {gather*} -x^{4} - x^{2} \log \relax (x)^{2} + 2 \, x^{3} + 7 \, x^{2} - 2 \, {\left (x^{3} - x^{2} - 4 \, x\right )} \log \relax (x) - 8 \, x - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.02, size = 50, normalized size = 2.27
method | result | size |
risch | \(-x^{2} \ln \relax (x )^{2}+\left (-2 x^{3}+2 x^{2}+8 x \right ) \ln \relax (x )-x^{4}+2 x^{3}+7 x^{2}-8 x -\ln \relax (x )\) | \(50\) |
default | \(-x^{2} \ln \relax (x )^{2}+2 x^{2} \ln \relax (x )+7 x^{2}-2 x^{3} \ln \relax (x )+2 x^{3}-x^{4}+8 x \ln \relax (x )-8 x -\ln \relax (x )\) | \(52\) |
norman | \(-x^{2} \ln \relax (x )^{2}+2 x^{2} \ln \relax (x )+7 x^{2}-2 x^{3} \ln \relax (x )+2 x^{3}-x^{4}+8 x \ln \relax (x )-8 x -\ln \relax (x )\) | \(52\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.34, size = 58, normalized size = 2.64 \begin {gather*} -x^{4} - 2 \, x^{3} \log \relax (x) - \frac {1}{2} \, {\left (2 \, \log \relax (x)^{2} - 2 \, \log \relax (x) + 1\right )} x^{2} + 2 \, x^{3} + x^{2} \log \relax (x) + \frac {15}{2} \, x^{2} + 8 \, x \log \relax (x) - 8 \, x - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.24, size = 51, normalized size = 2.32 \begin {gather*} -x^4-2\,x^3\,\ln \relax (x)+2\,x^3-x^2\,{\ln \relax (x)}^2+2\,x^2\,\ln \relax (x)+7\,x^2+8\,x\,\ln \relax (x)-8\,x-\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.18, size = 44, normalized size = 2.00 \begin {gather*} - x^{4} + 2 x^{3} - x^{2} \log {\relax (x )}^{2} + 7 x^{2} - 8 x + \left (- 2 x^{3} + 2 x^{2} + 8 x\right ) \log {\relax (x )} - \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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