Optimal. Leaf size=22 \[ \log \left (5 \left (-2 e^{50}+\frac {5}{16} x^5 \log ^4\left (\frac {4}{3}\right )\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 0.82, number of steps used = 2, number of rules used = 2, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12, 260} \begin {gather*} \log \left (32 e^{50}-5 x^5 \log ^4\left (\frac {4}{3}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 260
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\left (25 \log ^4\left (\frac {4}{3}\right )\right ) \int \frac {x^4}{-32 e^{50}+5 x^5 \log ^4\left (\frac {4}{3}\right )} \, dx\\ &=\log \left (32 e^{50}-5 x^5 \log ^4\left (\frac {4}{3}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 0.82 \begin {gather*} \log \left (-32 e^{50}+5 x^5 \log ^4\left (\frac {4}{3}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.03, size = 15, normalized size = 0.68 \begin {gather*} \log \left (5 \, x^{5} \log \left (\frac {3}{4}\right )^{4} - 32 \, e^{50}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 16, normalized size = 0.73 \begin {gather*} \log \left ({\left | 5 \, x^{5} \log \left (\frac {3}{4}\right )^{4} - 32 \, e^{50} \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.47, size = 15, normalized size = 0.68
method | result | size |
meijerg | \(\ln \left (1-\frac {5 x^{5} \ln \left (\frac {3}{4}\right )^{4} {\mathrm e}^{-50}}{32}\right )\) | \(15\) |
derivativedivides | \(\ln \left (5 x^{5} \ln \left (\frac {3}{4}\right )^{4}-32 \,{\mathrm e}^{50}\right )\) | \(18\) |
default | \(\ln \left (5 x^{5} \ln \left (\frac {3}{4}\right )^{4}-32 \,{\mathrm e}^{50}\right )\) | \(18\) |
norman | \(\ln \left (5 x^{5} \ln \left (\frac {3}{4}\right )^{4}-32 \,{\mathrm e}^{50}\right )\) | \(18\) |
risch | \(\frac {16 \ln \left (\left (80 \ln \relax (2)^{4}-160 \ln \relax (3) \ln \relax (2)^{3}+120 \ln \relax (3)^{2} \ln \relax (2)^{2}-40 \ln \relax (2) \ln \relax (3)^{3}+5 \ln \relax (3)^{4}\right ) x^{5}-32 \,{\mathrm e}^{50}\right ) \ln \relax (2)^{4}}{\ln \relax (3)^{4}-8 \ln \relax (2) \ln \relax (3)^{3}+24 \ln \relax (3)^{2} \ln \relax (2)^{2}-32 \ln \relax (3) \ln \relax (2)^{3}+16 \ln \relax (2)^{4}}-\frac {32 \ln \left (\left (80 \ln \relax (2)^{4}-160 \ln \relax (3) \ln \relax (2)^{3}+120 \ln \relax (3)^{2} \ln \relax (2)^{2}-40 \ln \relax (2) \ln \relax (3)^{3}+5 \ln \relax (3)^{4}\right ) x^{5}-32 \,{\mathrm e}^{50}\right ) \ln \relax (2)^{3} \ln \relax (3)}{\ln \relax (3)^{4}-8 \ln \relax (2) \ln \relax (3)^{3}+24 \ln \relax (3)^{2} \ln \relax (2)^{2}-32 \ln \relax (3) \ln \relax (2)^{3}+16 \ln \relax (2)^{4}}+\frac {24 \ln \left (\left (80 \ln \relax (2)^{4}-160 \ln \relax (3) \ln \relax (2)^{3}+120 \ln \relax (3)^{2} \ln \relax (2)^{2}-40 \ln \relax (2) \ln \relax (3)^{3}+5 \ln \relax (3)^{4}\right ) x^{5}-32 \,{\mathrm e}^{50}\right ) \ln \relax (2)^{2} \ln \relax (3)^{2}}{\ln \relax (3)^{4}-8 \ln \relax (2) \ln \relax (3)^{3}+24 \ln \relax (3)^{2} \ln \relax (2)^{2}-32 \ln \relax (3) \ln \relax (2)^{3}+16 \ln \relax (2)^{4}}-\frac {8 \ln \left (\left (80 \ln \relax (2)^{4}-160 \ln \relax (3) \ln \relax (2)^{3}+120 \ln \relax (3)^{2} \ln \relax (2)^{2}-40 \ln \relax (2) \ln \relax (3)^{3}+5 \ln \relax (3)^{4}\right ) x^{5}-32 \,{\mathrm e}^{50}\right ) \ln \relax (2) \ln \relax (3)^{3}}{\ln \relax (3)^{4}-8 \ln \relax (2) \ln \relax (3)^{3}+24 \ln \relax (3)^{2} \ln \relax (2)^{2}-32 \ln \relax (3) \ln \relax (2)^{3}+16 \ln \relax (2)^{4}}+\frac {\ln \left (\left (80 \ln \relax (2)^{4}-160 \ln \relax (3) \ln \relax (2)^{3}+120 \ln \relax (3)^{2} \ln \relax (2)^{2}-40 \ln \relax (2) \ln \relax (3)^{3}+5 \ln \relax (3)^{4}\right ) x^{5}-32 \,{\mathrm e}^{50}\right ) \ln \relax (3)^{4}}{\ln \relax (3)^{4}-8 \ln \relax (2) \ln \relax (3)^{3}+24 \ln \relax (3)^{2} \ln \relax (2)^{2}-32 \ln \relax (3) \ln \relax (2)^{3}+16 \ln \relax (2)^{4}}\) | \(479\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 15, normalized size = 0.68 \begin {gather*} \log \left (5 \, x^{5} \log \left (\frac {3}{4}\right )^{4} - 32 \, e^{50}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 15, normalized size = 0.68 \begin {gather*} \ln \left (5\,x^5\,{\ln \left (\frac {3}{4}\right )}^4-32\,{\mathrm {e}}^{50}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 2.82, size = 112, normalized size = 5.09 \begin {gather*} \frac {\left (- 800 \log {\relax (2 )}^{3} \log {\relax (3 )} - 200 \log {\relax (2 )} \log {\relax (3 )}^{3} + 25 \log {\relax (3 )}^{4} + 400 \log {\relax (2 )}^{4} + 600 \log {\relax (2 )}^{2} \log {\relax (3 )}^{2}\right ) \log {\left (x^{5} \left (- 160 \log {\relax (2 )}^{3} \log {\relax (3 )} - 40 \log {\relax (2 )} \log {\relax (3 )}^{3} + 5 \log {\relax (3 )}^{4} + 80 \log {\relax (2 )}^{4} + 120 \log {\relax (2 )}^{2} \log {\relax (3 )}^{2}\right ) - 32 e^{50} \right )}}{25 \left (- \log {\relax (3 )} + 2 \log {\relax (2 )}\right )^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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