Optimal. Leaf size=33 \[ \frac {-x+\frac {-\frac {5 e^5}{\frac {5}{x}+x^2}+\log (\log (3))}{x}}{\log (x)} \]
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Rubi [F]
time = 0.55, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {25 x^2+10 x^5+x^8+e^5 \left (25 x+5 x^4\right )+\left (-25 x^2+15 e^5 x^4-10 x^5-x^8\right ) \log (x)+\left (-25-10 x^3-x^6+\left (-25-10 x^3-x^6\right ) \log (x)\right ) \log (\log (3))}{\left (25 x^2+10 x^5+x^8\right ) \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {25 x^2+10 x^5+x^8+e^5 \left (25 x+5 x^4\right )+\left (-25 x^2+15 e^5 x^4-10 x^5-x^8\right ) \log (x)+\left (-25-10 x^3-x^6+\left (-25-10 x^3-x^6\right ) \log (x)\right ) \log (\log (3))}{x^2 \left (25+10 x^3+x^6\right ) \log ^2(x)} \, dx\\ &=\int \frac {25 x^2+10 x^5+x^8+e^5 \left (25 x+5 x^4\right )+\left (-25 x^2+15 e^5 x^4-10 x^5-x^8\right ) \log (x)+\left (-25-10 x^3-x^6+\left (-25-10 x^3-x^6\right ) \log (x)\right ) \log (\log (3))}{x^2 \left (5+x^3\right )^2 \log ^2(x)} \, dx\\ &=\int \left (\frac {5 e^5 x+5 x^2+x^5-5 \log (\log (3))-x^3 \log (\log (3))}{x^2 \left (5+x^3\right ) \log ^2(x)}+\frac {-25 x^2+15 e^5 x^4-10 x^5-x^8-25 \log (\log (3))-10 x^3 \log (\log (3))-x^6 \log (\log (3))}{x^2 \left (5+x^3\right )^2 \log (x)}\right ) \, dx\\ &=\int \frac {5 e^5 x+5 x^2+x^5-5 \log (\log (3))-x^3 \log (\log (3))}{x^2 \left (5+x^3\right ) \log ^2(x)} \, dx+\int \frac {-25 x^2+15 e^5 x^4-10 x^5-x^8-25 \log (\log (3))-10 x^3 \log (\log (3))-x^6 \log (\log (3))}{x^2 \left (5+x^3\right )^2 \log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 28, normalized size = 0.85 \begin {gather*} \frac {-x-\frac {5 e^5}{5+x^3}+\frac {\log (\log (3))}{x}}{\log (x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 20.60, size = 44, normalized size = 1.33
method | result | size |
risch | \(-\frac {x^{5}-x^{3} \ln \left (\ln \left (3\right )\right )+5 x \,{\mathrm e}^{5}+5 x^{2}-5 \ln \left (\ln \left (3\right )\right )}{x \left (x^{3}+5\right ) \ln \left (x \right )}\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 42, normalized size = 1.27 \begin {gather*} -\frac {x^{5} - x^{3} \log \left (\log \left (3\right )\right ) + 5 \, x^{2} + 5 \, x e^{5} - 5 \, \log \left (\log \left (3\right )\right )}{{\left (x^{4} + 5 \, x\right )} \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 39, normalized size = 1.18 \begin {gather*} -\frac {x^{5} + 5 \, x^{2} + 5 \, x e^{5} - {\left (x^{3} + 5\right )} \log \left (\log \left (3\right )\right )}{{\left (x^{4} + 5 \, x\right )} \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 39, normalized size = 1.18 \begin {gather*} \frac {- x^{5} + x^{3} \log {\left (\log {\left (3 \right )} \right )} - 5 x^{2} - 5 x e^{5} + 5 \log {\left (\log {\left (3 \right )} \right )}}{\left (x^{4} + 5 x\right ) \log {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 43, normalized size = 1.30 \begin {gather*} -\frac {x^{5} - x^{3} \log \left (\log \left (3\right )\right ) + 5 \, x^{2} + 5 \, x e^{5} - 5 \, \log \left (\log \left (3\right )\right )}{x^{4} \log \left (x\right ) + 5 \, x \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.55, size = 43, normalized size = 1.30 \begin {gather*} -\frac {x^5-\ln \left (\ln \left (3\right )\right )\,x^3+5\,x^2+5\,{\mathrm {e}}^5\,x-5\,\ln \left (\ln \left (3\right )\right )}{x\,\ln \left (x\right )\,\left (x^3+5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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