Optimal. Leaf size=22 \[ -\frac {1}{4}-(\log (x)-5 (-5-\log (4+\log (x))))^4 \]
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Rubi [A] time = 0.31, antiderivative size = 15, normalized size of antiderivative = 0.68, number of steps used = 4, number of rules used = 3, integrand size = 93, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {12, 6688, 6686} \begin {gather*} -(\log (x)+5 \log (\log (x)+4)+25)^4 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\operatorname {Subst}\left (\int -\frac {4 \left (140625+32500 x+2550 x^2+84 x^3+x^4+84375 \log (4+x)+16125 x \log (4+x)+885 x^2 \log (4+x)+15 x^3 \log (4+x)+16875 \log ^2(4+x)+2550 x \log ^2(4+x)+75 x^2 \log ^2(4+x)+1125 \log ^3(4+x)+125 x \log ^3(4+x)\right )}{4+x} \, dx,x,\log (x)\right )\\ &=-\left (4 \operatorname {Subst}\left (\int \frac {140625+32500 x+2550 x^2+84 x^3+x^4+84375 \log (4+x)+16125 x \log (4+x)+885 x^2 \log (4+x)+15 x^3 \log (4+x)+16875 \log ^2(4+x)+2550 x \log ^2(4+x)+75 x^2 \log ^2(4+x)+1125 \log ^3(4+x)+125 x \log ^3(4+x)}{4+x} \, dx,x,\log (x)\right )\right )\\ &=-\left (4 \operatorname {Subst}\left (\int \frac {(9+x) (25+x+5 \log (4+x))^3}{4+x} \, dx,x,\log (x)\right )\right )\\ &=-(25+\log (x)+5 \log (4+\log (x)))^4\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 16, normalized size = 0.73 \begin {gather*} -(\log (x)+5 (5+\log (4+\log (x))))^4 \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 1.04, size = 87, normalized size = 3.95 \begin {gather*} -\log \relax (x)^{4} - 500 \, {\left (\log \relax (x) + 25\right )} \log \left (\log \relax (x) + 4\right )^{3} - 625 \, \log \left (\log \relax (x) + 4\right )^{4} - 100 \, \log \relax (x)^{3} - 150 \, {\left (\log \relax (x)^{2} + 50 \, \log \relax (x) + 625\right )} \log \left (\log \relax (x) + 4\right )^{2} - 3750 \, \log \relax (x)^{2} - 20 \, {\left (\log \relax (x)^{3} + 75 \, \log \relax (x)^{2} + 1875 \, \log \relax (x) + 15625\right )} \log \left (\log \relax (x) + 4\right ) - 62500 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.24, size = 107, normalized size = 4.86 \begin {gather*} -{\left (\log \relax (x) + 4\right )}^{4} - 500 \, {\left (\log \relax (x) + 25\right )} \log \left (\log \relax (x) + 4\right )^{3} - 625 \, \log \left (\log \relax (x) + 4\right )^{4} - 84 \, {\left (\log \relax (x) + 4\right )}^{3} - 150 \, {\left ({\left (\log \relax (x) + 4\right )}^{2} + 42 \, \log \relax (x) + 609\right )} \log \left (\log \relax (x) + 4\right )^{2} - 2646 \, {\left (\log \relax (x) + 4\right )}^{2} - 20 \, {\left ({\left (\log \relax (x) + 4\right )}^{3} + 63 \, {\left (\log \relax (x) + 4\right )}^{2} + 1323 \, \log \relax (x) + 5292\right )} \log \left (\log \relax (x) + 4\right ) - 37044 \, \log \relax (x) - 185220 \, \log \left (\log \relax (x) + 4\right ) - 148176 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 97, normalized size = 4.41
method | result | size |
risch | \(-625 \ln \left (\ln \relax (x )+4\right )^{4}+\left (-500 \ln \relax (x )-12500\right ) \ln \left (\ln \relax (x )+4\right )^{3}+\left (-150 \ln \relax (x )^{2}-7500 \ln \relax (x )-93750\right ) \ln \left (\ln \relax (x )+4\right )^{2}+\left (-20 \ln \relax (x )^{3}-1500 \ln \relax (x )^{2}-37500 \ln \relax (x )\right ) \ln \left (\ln \relax (x )+4\right )-\ln \relax (x )^{4}-100 \ln \relax (x )^{3}-3750 \ln \relax (x )^{2}-62500 \ln \relax (x )-312500 \ln \left (\ln \relax (x )+4\right )\) | \(97\) |
default | \(-\ln \relax (x )^{4}-100 \ln \relax (x )^{3}-3750 \ln \relax (x )^{2}-62500 \ln \relax (x )-185220 \ln \left (\ln \relax (x )+4\right )-625 \ln \left (\ln \relax (x )+4\right )^{4}-500 \left (\ln \relax (x )+4\right ) \ln \left (\ln \relax (x )+4\right )^{3}-6300 \ln \left (\ln \relax (x )+4\right )^{2} \left (\ln \relax (x )+4\right )-26460 \ln \left (\ln \relax (x )+4\right ) \left (\ln \relax (x )+4\right )+\frac {349040}{3}-150 \left (\ln \relax (x )+4\right )^{2} \ln \left (\ln \relax (x )+4\right )^{2}-1260 \ln \left (\ln \relax (x )+4\right ) \left (\ln \relax (x )+4\right )^{2}-10500 \ln \left (\ln \relax (x )+4\right )^{3}-20 \ln \left (\ln \relax (x )+4\right ) \left (\ln \relax (x )+4\right )^{3}-66150 \ln \left (\ln \relax (x )+4\right )^{2}\) | \(137\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.38, size = 330, normalized size = 15.00 \begin {gather*} -30 \, \log \relax (x)^{3} \log \left (\log \relax (x) + 4\right )^{2} - 100 \, \log \relax (x)^{2} \log \left (\log \relax (x) + 4\right )^{3} - 125 \, \log \relax (x) \log \left (\log \relax (x) + 4\right )^{4} + \frac {10}{3} \, {\left (9 \, \log \left (\log \relax (x) + 4\right )^{2} - 6 \, \log \left (\log \relax (x) + 4\right ) + 2\right )} {\left (\log \relax (x) + 4\right )}^{3} - \log \relax (x)^{4} - 1770 \, \log \relax (x)^{2} \log \left (\log \relax (x) + 4\right )^{2} - 3400 \, \log \relax (x) \log \left (\log \relax (x) + 4\right )^{3} - 1125 \, \log \left (\log \relax (x) + 4\right )^{4} + 25 \, {\left (4 \, \log \left (\log \relax (x) + 4\right )^{3} - 6 \, \log \left (\log \relax (x) + 4\right )^{2} + 6 \, \log \left (\log \relax (x) + 4\right ) - 3\right )} {\left (\log \relax (x) + 4\right )}^{2} + 705 \, {\left (2 \, \log \left (\log \relax (x) + 4\right )^{2} - 2 \, \log \left (\log \relax (x) + 4\right ) + 1\right )} {\left (\log \relax (x) + 4\right )}^{2} - \frac {320}{3} \, \log \relax (x)^{3} - 32250 \, \log \relax (x) \log \left (\log \relax (x) + 4\right )^{2} - 22500 \, \log \left (\log \relax (x) + 4\right )^{3} + 125 \, {\left (\log \left (\log \relax (x) + 4\right )^{4} - 4 \, \log \left (\log \relax (x) + 4\right )^{3} + 12 \, \log \left (\log \relax (x) + 4\right )^{2} - 24 \, \log \left (\log \relax (x) + 4\right ) + 24\right )} {\left (\log \relax (x) + 4\right )} + 2600 \, {\left (\log \left (\log \relax (x) + 4\right )^{3} - 3 \, \log \left (\log \relax (x) + 4\right )^{2} + 6 \, \log \left (\log \relax (x) + 4\right ) - 6\right )} {\left (\log \relax (x) + 4\right )} + 19530 \, {\left (\log \left (\log \relax (x) + 4\right )^{2} - 2 \, \log \left (\log \relax (x) + 4\right ) + 2\right )} {\left (\log \relax (x) + 4\right )} - 4460 \, \log \relax (x)^{2} + 130000 \, {\left (\log \relax (x) + 4\right )} \log \left (\log \relax (x) + 4\right ) - 130000 \, \log \relax (x) \log \left (\log \relax (x) + 4\right ) - 168750 \, \log \left (\log \relax (x) + 4\right )^{2} - 94320 \, \log \relax (x) - 705220 \, \log \left (\log \relax (x) + 4\right ) - 520000 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.07, size = 99, normalized size = 4.50 \begin {gather*} -312500\,\ln \left (\ln \relax (x)+4\right )-62500\,\ln \relax (x)-625\,{\ln \left (\ln \relax (x)+4\right )}^4-{\ln \left (\ln \relax (x)+4\right )}^3\,\left (500\,\ln \relax (x)+12500\right )-3750\,{\ln \relax (x)}^2-100\,{\ln \relax (x)}^3-{\ln \relax (x)}^4-{\ln \left (\ln \relax (x)+4\right )}^2\,\left (150\,{\ln \relax (x)}^2+7500\,\ln \relax (x)+93750\right )-\ln \left (\ln \relax (x)+4\right )\,\left (20\,{\ln \relax (x)}^3+1500\,{\ln \relax (x)}^2+37500\,\ln \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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