Optimal. Leaf size=20 \[ \frac {\left (19+\frac {x}{5}-\log ^2(x)\right )^2}{\log (x)} \]
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Rubi [B] time = 0.35, antiderivative size = 42, normalized size of antiderivative = 2.10, number of steps used = 22, number of rules used = 13, integrand size = 56, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.232, Rules used = {12, 6742, 43, 2353, 2297, 2298, 2302, 30, 2306, 2309, 2178, 2330, 2295} \begin {gather*} \frac {x^2}{25 \log (x)}+\log ^3(x)-\frac {2}{5} x \log (x)-38 \log (x)+\frac {38 x}{5 \log (x)}+\frac {361}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 43
Rule 2178
Rule 2295
Rule 2297
Rule 2298
Rule 2302
Rule 2306
Rule 2309
Rule 2330
Rule 2353
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{25} \int \frac {-9025-190 x-x^2+\left (190 x+2 x^2\right ) \log (x)+(-950-10 x) \log ^2(x)-10 x \log ^3(x)+75 \log ^4(x)}{x \log ^2(x)} \, dx\\ &=\frac {1}{25} \int \left (-\frac {10 (95+x)}{x}-\frac {(95+x)^2}{x \log ^2(x)}+\frac {2 (95+x)}{\log (x)}-10 \log (x)+\frac {75 \log ^2(x)}{x}\right ) \, dx\\ &=-\left (\frac {1}{25} \int \frac {(95+x)^2}{x \log ^2(x)} \, dx\right )+\frac {2}{25} \int \frac {95+x}{\log (x)} \, dx-\frac {2}{5} \int \frac {95+x}{x} \, dx-\frac {2}{5} \int \log (x) \, dx+3 \int \frac {\log ^2(x)}{x} \, dx\\ &=\frac {2 x}{5}-\frac {2}{5} x \log (x)-\frac {1}{25} \int \left (\frac {190}{\log ^2(x)}+\frac {9025}{x \log ^2(x)}+\frac {x}{\log ^2(x)}\right ) \, dx+\frac {2}{25} \int \left (\frac {95}{\log (x)}+\frac {x}{\log (x)}\right ) \, dx-\frac {2}{5} \int \left (1+\frac {95}{x}\right ) \, dx+3 \operatorname {Subst}\left (\int x^2 \, dx,x,\log (x)\right )\\ &=-38 \log (x)-\frac {2}{5} x \log (x)+\log ^3(x)-\frac {1}{25} \int \frac {x}{\log ^2(x)} \, dx+\frac {2}{25} \int \frac {x}{\log (x)} \, dx-\frac {38}{5} \int \frac {1}{\log ^2(x)} \, dx+\frac {38}{5} \int \frac {1}{\log (x)} \, dx-361 \int \frac {1}{x \log ^2(x)} \, dx\\ &=\frac {38 x}{5 \log (x)}+\frac {x^2}{25 \log (x)}-38 \log (x)-\frac {2}{5} x \log (x)+\log ^3(x)+\frac {38 \text {li}(x)}{5}-\frac {2}{25} \int \frac {x}{\log (x)} \, dx+\frac {2}{25} \operatorname {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )-\frac {38}{5} \int \frac {1}{\log (x)} \, dx-361 \operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log (x)\right )\\ &=\frac {2}{25} \text {Ei}(2 \log (x))+\frac {361}{\log (x)}+\frac {38 x}{5 \log (x)}+\frac {x^2}{25 \log (x)}-38 \log (x)-\frac {2}{5} x \log (x)+\log ^3(x)-\frac {2}{25} \operatorname {Subst}\left (\int \frac {e^{2 x}}{x} \, dx,x,\log (x)\right )\\ &=\frac {361}{\log (x)}+\frac {38 x}{5 \log (x)}+\frac {x^2}{25 \log (x)}-38 \log (x)-\frac {2}{5} x \log (x)+\log ^3(x)\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.02, size = 42, normalized size = 2.10 \begin {gather*} \frac {361}{\log (x)}+\frac {38 x}{5 \log (x)}+\frac {x^2}{25 \log (x)}-38 \log (x)-\frac {2}{5} x \log (x)+\log ^3(x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.88, size = 29, normalized size = 1.45 \begin {gather*} \frac {25 \, \log \relax (x)^{4} - 10 \, {\left (x + 95\right )} \log \relax (x)^{2} + x^{2} + 190 \, x + 9025}{25 \, \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 28, normalized size = 1.40 \begin {gather*} \log \relax (x)^{3} - \frac {2}{5} \, x \log \relax (x) + \frac {x^{2} + 190 \, x + 9025}{25 \, \log \relax (x)} - 38 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 29, normalized size = 1.45
method | result | size |
risch | \(\ln \relax (x )^{3}-\frac {2 x \ln \relax (x )}{5}-38 \ln \relax (x )+\frac {x^{2}+190 x +9025}{25 \ln \relax (x )}\) | \(29\) |
norman | \(\frac {361+\ln \relax (x )^{4}-38 \ln \relax (x )^{2}+\frac {38 x}{5}+\frac {x^{2}}{25}-\frac {2 x \ln \relax (x )^{2}}{5}}{\ln \relax (x )}\) | \(33\) |
default | \(\ln \relax (x )^{3}-\frac {2 x \ln \relax (x )}{5}-38 \ln \relax (x )+\frac {x^{2}}{25 \ln \relax (x )}+\frac {38 x}{5 \ln \relax (x )}+\frac {361}{\ln \relax (x )}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.39, size = 48, normalized size = 2.40 \begin {gather*} \log \relax (x)^{3} - \frac {2}{5} \, x \log \relax (x) + \frac {361}{\log \relax (x)} + \frac {2}{25} \, {\rm Ei}\left (2 \, \log \relax (x)\right ) + \frac {38}{5} \, {\rm Ei}\left (\log \relax (x)\right ) - \frac {38}{5} \, \Gamma \left (-1, -\log \relax (x)\right ) - \frac {2}{25} \, \Gamma \left (-1, -2 \, \log \relax (x)\right ) - 38 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 8.86, size = 17, normalized size = 0.85 \begin {gather*} \frac {{\left (-5\,{\ln \relax (x)}^2+x+95\right )}^2}{25\,\ln \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.13, size = 31, normalized size = 1.55 \begin {gather*} - \frac {2 x \log {\relax (x )}}{5} + \frac {x^{2} + 190 x + 9025}{25 \log {\relax (x )}} + \log {\relax (x )}^{3} - 38 \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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