Optimal. Leaf size=29 \[ -4-e^4+\frac {1-x}{x}-x+\log (x)-\log (2+2 x) \]
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Rubi [A] time = 0.04, antiderivative size = 15, normalized size of antiderivative = 0.52, number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {1593, 1620} \begin {gather*} -x+\frac {1}{x}+\log (x)-\log (x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 1593
Rule 1620
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-1-x^2-x^3}{x^2 (1+x)} \, dx\\ &=\int \left (-1+\frac {1}{-1-x}-\frac {1}{x^2}+\frac {1}{x}\right ) \, dx\\ &=\frac {1}{x}-x+\log (x)-\log (1+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 0.52 \begin {gather*} \frac {1}{x}-x+\log (x)-\log (1+x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 21, normalized size = 0.72 \begin {gather*} -\frac {x^{2} + x \log \left (x + 1\right ) - x \log \relax (x) - 1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 17, normalized size = 0.59 \begin {gather*} -x + \frac {1}{x} - \log \left ({\left | x + 1 \right |}\right ) + \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 16, normalized size = 0.55
method | result | size |
default | \(-x +\ln \relax (x )+\frac {1}{x}-\ln \left (x +1\right )\) | \(16\) |
meijerg | \(-x +\ln \relax (x )+\frac {1}{x}-\ln \left (x +1\right )\) | \(16\) |
risch | \(-x +\ln \relax (x )+\frac {1}{x}-\ln \left (x +1\right )\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 15, normalized size = 0.52 \begin {gather*} -x + \frac {1}{x} - \log \left (x + 1\right ) + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 15, normalized size = 0.52 \begin {gather*} \frac {1}{x}-2\,\mathrm {atanh}\left (2\,x+1\right )-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 12, normalized size = 0.41 \begin {gather*} - x + \log {\relax (x )} - \log {\left (x + 1 \right )} + \frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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