Optimal. Leaf size=29 \[ \log \left (e^x (3-x)-\frac {1}{2} e^x \left (\frac {5}{x}+9 x^2\right )\right ) \]
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Rubi [A]
time = 0.06, antiderivative size = 22, normalized size of antiderivative = 0.76, number of steps
used = 3, number of rules used = 2, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {2099, 1601}
\begin {gather*} \log \left (9 x^3+2 x^2-6 x+5\right )+x-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 1601
Rule 2099
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-\frac {1}{x}+\frac {-6+4 x+27 x^2}{5-6 x+2 x^2+9 x^3}\right ) \, dx\\ &=x-\log (x)+\int \frac {-6+4 x+27 x^2}{5-6 x+2 x^2+9 x^3} \, dx\\ &=x-\log (x)+\log \left (5-6 x+2 x^2+9 x^3\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 22, normalized size = 0.76 \begin {gather*} x-\log (x)+\log \left (5-6 x+2 x^2+9 x^3\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 23, normalized size = 0.79
method | result | size |
default | \(x +\ln \left (9 x^{3}+2 x^{2}-6 x +5\right )-\ln \left (x \right )\) | \(23\) |
norman | \(x +\ln \left (9 x^{3}+2 x^{2}-6 x +5\right )-\ln \left (x \right )\) | \(23\) |
risch | \(x +\ln \left (9 x^{3}+2 x^{2}-6 x +5\right )-\ln \left (x \right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 22, normalized size = 0.76 \begin {gather*} x + \log \left (9 \, x^{3} + 2 \, x^{2} - 6 \, x + 5\right ) - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 22, normalized size = 0.76 \begin {gather*} x + \log \left (9 \, x^{3} + 2 \, x^{2} - 6 \, x + 5\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 = 20, normalized size = 0.69 \begin {gather*} x - \log {\left (x \right )} + \log {\left (9 x^{3} + 2 x^{2} - 6 x + 5 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 24, normalized size = 0.83 \begin {gather*} x + \log \left ({\left | 9 \, x^{3} + 2 \, x^{2} - 6 \, x + 5 \right |}\right ) - \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 = 0.13, size = 22, normalized size = 0.76 \begin {gather*} x+\ln \left (9\,x^3+2\,x^2-6\,x+5\right )-\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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