Optimal. Leaf size=21 \[ 6-x^2+4 \left (-\frac {12}{x^2}+\log \left (x+x^2\right )\right ) \]
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Rubi [A]
time = 0.03, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.057, Rules used = {1607, 1634}
\begin {gather*} -x^2-\frac {48}{x^2}+4 \log (x)+4 \log (x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 1607
Rule 1634
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {96+96 x+4 x^2+8 x^3-2 x^4-2 x^5}{x^3 (1+x)} \, dx\\ &=\int \left (\frac {96}{x^3}+\frac {4}{x}-2 x+\frac {4}{1+x}\right ) \, dx\\ &=-\frac {48}{x^2}-x^2+4 \log (x)+4 \log (1+x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 21, normalized size = 1.00 \begin {gather*} -\frac {48}{x^2}-x^2+4 \log (x)+4 \log (1+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.38, size = 22, normalized size = 1.05
method | result | size |
risch | \(-x^{2}-\frac {48}{x^{2}}+4 \ln \left (x^{2}+x \right )\) | \(20\) |
default | \(-x^{2}+4 \ln \left (x +1\right )-\frac {48}{x^{2}}+4 \ln \left (x \right )\) | \(22\) |
norman | \(\frac {-x^{4}-48}{x^{2}}+4 \ln \left (x \right )+4 \ln \left (x +1\right )\) | \(23\) |
meijerg | \(\frac {x \left (-3 x +6\right )}{3}-2 x +4 \ln \left (x +1\right )+4 \ln \left (x \right )-\frac {48}{x^{2}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 21, normalized size = 1.00 \begin {gather*} -x^{2} - \frac {48}{x^{2}} + 4 \, \log \left (x + 1\right ) + 4 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 21, normalized size = 1.00 \begin {gather*} -\frac {x^{4} - 4 \, x^{2} \log \left (x^{2} + x\right ) + 48}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 15, normalized size = 0.71 \begin {gather*} - x^{2} + 4 \log {\left (x^{2} + x \right )} - \frac {48}{x^{2}} \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 = 1.10 \begin {gather*} -x^{2} - \frac {48}{x^{2}} + 4 \, \log \left ({\left | x + 1 \right |}\right ) + 4 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 19, normalized size = 0.90 \begin {gather*} 4\,\ln \left (x\,\left (x+1\right )\right )-\frac {48}{x^2}-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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