Optimal. Leaf size=17 \[ 6+\frac {3 e^5}{-3+x}-x+\log (25) \]
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Rubi [A]
time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps
used = 3, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {27, 697}
\begin {gather*} -x-\frac {3 e^5}{3-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 697
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-9-3 e^5+6 x-x^2}{(-3+x)^2} \, dx\\ &=\int \left (-1-\frac {3 e^5}{(-3+x)^2}\right ) \, dx\\ &=-\frac {3 e^5}{3-x}-x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 0.82 \begin {gather*} \frac {3 e^5}{-3+x}-x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.35, size = 14, normalized size = 0.82
method | result | size |
default | \(-x +\frac {3 \,{\mathrm e}^{5}}{x -3}\) | \(14\) |
risch | \(-x +\frac {3 \,{\mathrm e}^{5}}{x -3}\) | \(14\) |
gosper | \(\frac {-x^{2}+3 \,{\mathrm e}^{5}+9}{x -3}\) | \(18\) |
meijerg | \(\frac {x}{1-\frac {x}{3}}-\frac {{\mathrm e}^{5} x}{3 \left (1-\frac {x}{3}\right )}-\frac {x \left (-x +6\right )}{3 \left (1-\frac {x}{3}\right )}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 13, normalized size = 0.76 \begin {gather*} -x + \frac {3 \, e^{5}}{x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 18, normalized size = 1.06 \begin {gather*} -\frac {x^{2} - 3 \, x - 3 \, e^{5}}{x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 8, normalized size = 0.47 \begin {gather*} - x + \frac {3 e^{5}}{x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 13, normalized size = 0.76 \begin {gather*} -x + \frac {3 \, e^{5}}{x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 13, normalized size = 0.76 \begin {gather*} \frac {3\,{\mathrm {e}}^5}{x-3}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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