Optimal. Leaf size=30 \[ x^2+4 \left (-6-\frac {e}{-1+\left (-5+\frac {5-x}{x}\right ) x}+\log (3)\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 14, normalized size of antiderivative = 0.47, number of steps used = 3, number of rules used = 2, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {27, 1850} \begin {gather*} x^2-\frac {2 e}{2-3 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 1850
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-6 e+8 x-24 x^2+18 x^3}{(-2+3 x)^2} \, dx\\ &=\int \left (2 x-\frac {6 e}{(-2+3 x)^2}\right ) \, dx\\ &=-\frac {2 e}{2-3 x}+x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 0.93 \begin {gather*} \frac {18 e+(2-3 x)^2 (2+3 x)}{9 (-2+3 x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.12, size = 23, normalized size = 0.77 \begin {gather*} \frac {3 \, x^{3} - 2 \, x^{2} + 2 \, e}{3 \, x - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 15, normalized size = 0.50 \begin {gather*} x^{2} + \frac {2 \, e}{3 \, x - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.30, size = 14, normalized size = 0.47
method | result | size |
risch | \(x^{2}+\frac {2 \,{\mathrm e}}{3 \left (x -\frac {2}{3}\right )}\) | \(14\) |
default | \(x^{2}+\frac {2 \,{\mathrm e}}{3 x -2}\) | \(16\) |
gosper | \(\frac {3 x^{3}-2 x^{2}+2 \,{\mathrm e}}{3 x -2}\) | \(24\) |
norman | \(\frac {3 x \,{\mathrm e}-2 x^{2}+3 x^{3}}{3 x -2}\) | \(25\) |
meijerg | \(-\frac {3 \,{\mathrm e} x}{2 \left (1-\frac {3 x}{2}\right )}+\frac {x \left (-\frac {9}{2} x^{2}-9 x +12\right )}{3-\frac {9 x}{2}}-\frac {8 x \left (-\frac {9 x}{2}+6\right )}{9 \left (1-\frac {3 x}{2}\right )}+\frac {4 x}{3 \left (1-\frac {3 x}{2}\right )}\) | \(59\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 15, normalized size = 0.50 \begin {gather*} x^{2} + \frac {2 \, e}{3 \, x - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 15, normalized size = 0.50 \begin {gather*} \frac {2\,\mathrm {e}}{3\,x-2}+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 12, normalized size = 0.40 \begin {gather*} x^{2} + \frac {2 e}{3 x - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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