Optimal. Leaf size=27 \[ e^3+x \left (3+4 \left (-3-x+\frac {4 e^4}{-1+3 x}\right )\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 23, normalized size of antiderivative = 0.85, number of steps used = 3, number of rules used = 2, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {27, 1850} \begin {gather*} -4 x^2-9 x-\frac {16 e^4}{3 (1-3 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 {-9-16 e^4+46 x-33 x^2-72 x^3}{(-1+3 x)^2} \, dx\\ &=\int \left (-9-8 x-\frac {16 e^4}{(-1+3 x)^2}\right ) \, dx\\ &=-\frac {16 e^4}{3 (1-3 x)}-9 x-4 x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 23, normalized size = 0.85 \begin {gather*} -\frac {16 e^4}{3 (1-3 x)}-9 x-4 x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 27, normalized size = 1.00 \begin {gather*} -\frac {36 \, x^{3} + 69 \, x^{2} - 27 \, x - 16 \, e^{4}}{3 \, {\left (3 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 20, normalized size = 0.74 \begin {gather*} -4 \, x^{2} - 9 \, x + \frac {16 \, e^{4}}{3 \, {\left (3 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.41, size = 19, normalized size = 0.70
method | result | size |
risch | \(-4 x^{2}-9 x +\frac {16 \,{\mathrm e}^{4}}{9 \left (x -\frac {1}{3}\right )}\) | \(19\) |
default | \(-4 x^{2}-9 x +\frac {16 \,{\mathrm e}^{4}}{3 \left (3 x -1\right )}\) | \(21\) |
norman | \(\frac {-23 x^{2}-12 x^{3}+3+\frac {16 \,{\mathrm e}^{4}}{3}}{3 x -1}\) | \(25\) |
gosper | \(\frac {-36 x^{3}-69 x^{2}+16 \,{\mathrm e}^{4}+9}{9 x -3}\) | \(26\) |
meijerg | \(-\frac {16 \,{\mathrm e}^{4} x}{-3 x +1}-\frac {2 x \left (-18 x^{2}-18 x +12\right )}{3 \left (-3 x +1\right )}-\frac {11 x \left (-9 x +6\right )}{9 \left (-3 x +1\right )}+\frac {19 x}{3 \left (-3 x +1\right )}\) | \(59\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 20, normalized size = 0.74 \begin {gather*} -4 \, x^{2} - 9 \, x + \frac {16 \, e^{4}}{3 \, {\left (3 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 20, normalized size = 0.74 \begin {gather*} \frac {16\,{\mathrm {e}}^4}{3\,\left (3\,x-1\right )}-9\,x-4\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 17, normalized size = 0.63 \begin {gather*} - 4 x^{2} - 9 x + \frac {16 e^{4}}{9 x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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