Optimal. Leaf size=17 \[ (3 \log (x)+\log (4-x+3 e x))^4 \]
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Rubi [A] time = 0.39, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 5, integrand size = 103, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {6, 1593, 6688, 12, 6686} \begin {gather*} (3 \log (x)+\log (3 e x-x+4))^4 \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 1593
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {(1296-432 x+1296 e x) \log ^3(x)+(1296-432 x+1296 e x) \log ^2(x) \log (4-x+3 e x)+(432-144 x+432 e x) \log (x) \log ^2(4-x+3 e x)+(48-16 x+48 e x) \log ^3(4-x+3 e x)}{4 x+(-1+3 e) x^2} \, dx\\ &=\int \frac {(1296-432 x+1296 e x) \log ^3(x)+(1296-432 x+1296 e x) \log ^2(x) \log (4-x+3 e x)+(432-144 x+432 e x) \log (x) \log ^2(4-x+3 e x)+(48-16 x+48 e x) \log ^3(4-x+3 e x)}{x (4+(-1+3 e) x)} \, dx\\ &=\int \frac {16 (3+(-1+3 e) x) (3 \log (x)+\log (4-x+3 e x))^3}{x (4+(-1+3 e) x)} \, dx\\ &=16 \int \frac {(3+(-1+3 e) x) (3 \log (x)+\log (4-x+3 e x))^3}{x (4+(-1+3 e) x)} \, dx\\ &=(3 \log (x)+\log (4-x+3 e x))^4\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 17, normalized size = 1.00 \begin {gather*} (3 \log (x)+\log (4-x+3 e x))^4 \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 1.14, size = 73, normalized size = 4.29 \begin {gather*} \log \left (3 \, x e - x + 4\right )^{4} + 12 \, \log \left (3 \, x e - x + 4\right )^{3} \log \relax (x) + 54 \, \log \left (3 \, x e - x + 4\right )^{2} \log \relax (x)^{2} + 108 \, \log \left (3 \, x e - x + 4\right ) \log \relax (x)^{3} + 81 \, \log \relax (x)^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.18, size = 75, normalized size = 4.41 \begin {gather*} 4 \, \log \left (3 \, x e - x + 4\right )^{4} + 12 \, \log \left (3 \, x e - x + 4\right )^{3} \log \relax (x) + 54 \, \log \left (3 \, x e - x + 4\right )^{2} \log \relax (x)^{2} + 108 \, \log \left (3 \, x e - x + 4\right ) \log \relax (x)^{3} + 81 \, \log \relax (x)^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.14, size = 74, normalized size = 4.35
method | result | size |
risch | \(81 \ln \relax (x )^{4}+108 \ln \relax (x )^{3} \ln \left (3 x \,{\mathrm e}-x +4\right )+54 \ln \relax (x )^{2} \ln \left (3 x \,{\mathrm e}-x +4\right )^{2}+12 \ln \relax (x ) \ln \left (3 x \,{\mathrm e}-x +4\right )^{3}+\ln \left (3 x \,{\mathrm e}-x +4\right )^{4}\) | \(74\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.42, size = 73, normalized size = 4.29 \begin {gather*} \log \left (x {\left (3 \, e - 1\right )} + 4\right )^{4} + 12 \, \log \left (x {\left (3 \, e - 1\right )} + 4\right )^{3} \log \relax (x) + 54 \, \log \left (x {\left (3 \, e - 1\right )} + 4\right )^{2} \log \relax (x)^{2} + 108 \, \log \left (x {\left (3 \, e - 1\right )} + 4\right ) \log \relax (x)^{3} + 81 \, \log \relax (x)^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.76, size = 73, normalized size = 4.29 \begin {gather*} {\ln \left (3\,x\,\mathrm {e}-x+4\right )}^4+12\,{\ln \left (3\,x\,\mathrm {e}-x+4\right )}^3\,\ln \relax (x)+54\,{\ln \left (3\,x\,\mathrm {e}-x+4\right )}^2\,{\ln \relax (x)}^2+108\,\ln \left (3\,x\,\mathrm {e}-x+4\right )\,{\ln \relax (x)}^3+81\,{\ln \relax (x)}^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 4.92, size = 76, normalized size = 4.47 \begin {gather*} 81 \log {\relax (x )}^{4} + 108 \log {\relax (x )}^{3} \log {\left (- x + 3 e x + 4 \right )} + 54 \log {\relax (x )}^{2} \log {\left (- x + 3 e x + 4 \right )}^{2} + 12 \log {\relax (x )} \log {\left (- x + 3 e x + 4 \right )}^{3} + \log {\left (- x + 3 e x + 4 \right )}^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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