Optimal. Leaf size=17 \[ \frac {-5-5 x^2}{(1+x)^2 \log (x)} \]
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Rubi [F]
time = 0.75, 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 {5+5 x+5 x^2+5 x^3+\left (10 x-10 x^2\right ) \log (x)}{\left (x+3 x^2+3 x^3+x^4\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 {5 \left (1+x+x^2+x^3-2 (-1+x) x \log (x)\right )}{x (1+x)^3 \log ^2(x)} \, dx\\ &=5 \int \frac {1+x+x^2+x^3-2 (-1+x) x \log (x)}{x (1+x)^3 \log ^2(x)} \, dx\\ &=5 \int \left (\frac {1+x^2}{x (1+x)^2 \log ^2(x)}-\frac {2 (-1+x)}{(1+x)^3 \log (x)}\right ) \, dx\\ &=5 \int \frac {1+x^2}{x (1+x)^2 \log ^2(x)} \, dx-10 \int \frac {-1+x}{(1+x)^3 \log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 18, normalized size = 1.06 \begin {gather*} \frac {5 \left (-1-x^2\right )}{(1+x)^2 \log (x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 11.38, size = 18, normalized size = 1.06
method | result | size |
norman | \(\frac {-5 x^{2}-5}{\ln \left (x \right ) \left (x +1\right )^{2}}\) | \(18\) |
risch | \(-\frac {5 \left (x^{2}+1\right )}{\left (x^{2}+2 x +1\right ) \ln \left (x \right )}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 21, normalized size = 1.24 \begin {gather*} -\frac {5 \, {\left (x^{2} + 1\right )}}{{\left (x^{2} + 2 \, x + 1\right )} \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 21, normalized size = 1.24 \begin {gather*} -\frac {5 \, {\left (x^{2} + 1\right )}}{{\left (x^{2} + 2 \, x + 1\right )} \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 19, normalized size = 1.12 \begin {gather*} \frac {- 5 x^{2} - 5}{\left (x^{2} + 2 x + 1\right ) \log {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 23, normalized size = 1.35 \begin {gather*} -\frac {5 \, {\left (x^{2} + 1\right )}}{x^{2} \log \left (x\right ) + 2 \, x \log \left (x\right ) + \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.99, size = 16, normalized size = 0.94 \begin {gather*} -\frac {5\,\left (x^2+1\right )}{\ln \left (x\right )\,{\left (x+1\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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