Optimal. Leaf size=15 \[ x+\frac {x^2}{2}+\log (1-x) \]
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Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {45}
\begin {gather*} \frac {x^2}{2}+x+\log (1-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\int \left (1+\frac {1}{-1+x}+x\right ) \, dx\\ &=x+\frac {x^2}{2}+\log (1-x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 1.07 \begin {gather*} -\frac {3}{2}+x+\frac {x^2}{2}+\log (-1+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 12, normalized size = 0.80
method | result | size |
default | \(\frac {x^{2}}{2}+x +\ln \left (x -1\right )\) | \(12\) |
norman | \(\frac {x^{2}}{2}+x +\ln \left (x -1\right )\) | \(12\) |
risch | \(\frac {x^{2}}{2}+x +\ln \left (x -1\right )\) | \(12\) |
parallelrisch | \(\frac {x^{2}}{2}+x +\ln \left (x -1\right )\) | \(12\) |
meijerg | \(\frac {x \left (3 x +6\right )}{6}+\ln \left (1-x \right )\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.37, size = 11, normalized size = 0.73 \begin {gather*} \frac {1}{2} \, x^{2} + x + \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.58, size = 11, normalized size = 0.73 \begin {gather*} \frac {1}{2} \, x^{2} + x + \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 10, normalized size = 0.67 \begin {gather*} \frac {x^{2}}{2} + x + \log {\left (x - 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.48, size = 12, normalized size = 0.80 \begin {gather*} \frac {1}{2} \, x^{2} + x + \log \left ({\left | x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 11, normalized size = 0.73 \begin {gather*} x+\ln \left (x-1\right )+\frac {x^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F] Failed to verify
time = 1.00, size = 20, normalized size = 1.33 \begin {gather*} -\frac {x^{3}}{3}-\frac {x^{2}}{2}-x -\ln \left (x -1\right ) \end {gather*}
Warning: Unable to verify antiderivative.
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