Optimal. Leaf size=17 \[ \frac {5 x}{-4+\frac {625}{2 x^4}+x+\log (x)} \]
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Rubi [F]
time = 1.08, 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 {31250 x^4-100 x^8+20 x^8 \log (x)}{390625-10000 x^4+2500 x^5+64 x^8-32 x^9+4 x^{10}+\left (2500 x^4-32 x^8+8 x^9\right ) \log (x)+4 x^8 \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 {10 x^4 \left (3125-10 x^4+2 x^4 \log (x)\right )}{\left (625-8 x^4+2 x^5+2 x^4 \log (x)\right )^2} \, dx\\ &=10 \int \frac {x^4 \left (3125-10 x^4+2 x^4 \log (x)\right )}{\left (625-8 x^4+2 x^5+2 x^4 \log (x)\right )^2} \, dx\\ &=10 \int \left (-\frac {2 x^4 \left (-1250+x^4+x^5\right )}{\left (625-8 x^4+2 x^5+2 x^4 \log (x)\right )^2}+\frac {x^4}{625-8 x^4+2 x^5+2 x^4 \log (x)}\right ) \, dx\\ &=10 \int \frac {x^4}{625-8 x^4+2 x^5+2 x^4 \log (x)} \, dx-20 \int \frac {x^4 \left (-1250+x^4+x^5\right )}{\left (625-8 x^4+2 x^5+2 x^4 \log (x)\right )^2} \, dx\\ &=10 \int \frac {x^4}{625-8 x^4+2 x^5+2 x^4 \log (x)} \, dx-20 \int \left (-\frac {1250 x^4}{\left (625-8 x^4+2 x^5+2 x^4 \log (x)\right )^2}+\frac {x^8}{\left (625-8 x^4+2 x^5+2 x^4 \log (x)\right )^2}+\frac {x^9}{\left (625-8 x^4+2 x^5+2 x^4 \log (x)\right )^2}\right ) \, dx\\ &=10 \int \frac {x^4}{625-8 x^4+2 x^5+2 x^4 \log (x)} \, dx-20 \int \frac {x^8}{\left (625-8 x^4+2 x^5+2 x^4 \log (x)\right )^2} \, dx-20 \int \frac {x^9}{\left (625-8 x^4+2 x^5+2 x^4 \log (x)\right )^2} \, dx+25000 \int \frac {x^4}{\left (625-8 x^4+2 x^5+2 x^4 \log (x)\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.10, size = 26, normalized size = 1.53 \begin {gather*} \frac {10 x^5}{625-8 x^4+2 x^5+2 x^4 \log (x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(37\) vs.
\(2(15)=30\).
time = 0.73, size = 38, normalized size = 2.24
method | result | size |
risch | \(\frac {10 x^{5}}{2 x^{4} \ln \left (x \right )+2 x^{5}-8 x^{4}+625}\) | \(27\) |
default | \(-\frac {5 \left (2 x^{4} \ln \left (x \right )-8 x^{4}+625\right )}{2 x^{4} \ln \left (x \right )+2 x^{5}-8 x^{4}+625}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 26, normalized size = 1.53 \begin {gather*} \frac {10 \, x^{5}}{2 \, x^{5} + 2 \, x^{4} \log \left (x\right ) - 8 \, x^{4} + 625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 26, normalized size = 1.53 \begin {gather*} \frac {10 \, x^{5}}{2 \, x^{5} + 2 \, x^{4} \log \left (x\right ) - 8 \, x^{4} + 625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 24, normalized size = 1.41 \begin {gather*} \frac {10 x^{5}}{2 x^{5} + 2 x^{4} \log {\left (x \right )} - 8 x^{4} + 625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 26, normalized size = 1.53 \begin {gather*} \frac {10 \, x^{5}}{2 \, x^{5} + 2 \, x^{4} \log \left (x\right ) - 8 \, x^{4} + 625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.15, size = 26, normalized size = 1.53 \begin {gather*} \frac {10\,x^5}{2\,x^4\,\ln \left (x\right )-8\,x^4+2\,x^5+625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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