Optimal. Leaf size=17 \[ 2 \left (-2-\frac {e^x}{-5+x}+3 x\right ) \]
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Rubi [A] time = 0.08, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps used = 4, number of rules used = 3, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {27, 6688, 2197} \begin {gather*} 6 x+\frac {2 e^x}{5-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 2197
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {150+e^x (12-2 x)-60 x+6 x^2}{(-5+x)^2} \, dx\\ &=\int \left (6-\frac {2 e^x (-6+x)}{(-5+x)^2}\right ) \, dx\\ &=6 x-2 \int \frac {e^x (-6+x)}{(-5+x)^2} \, dx\\ &=\frac {2 e^x}{5-x}+6 x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 14, normalized size = 0.82 \begin {gather*} -\frac {2 e^x}{-5+x}+6 x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.44, size = 20, normalized size = 1.18 \begin {gather*} \frac {2 \, {\left (3 \, x^{2} - 15 \, x - e^{x}\right )}}{x - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 20, normalized size = 1.18 \begin {gather*} \frac {2 \, {\left (3 \, x^{2} - 15 \, x - e^{x}\right )}}{x - 5} \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 = 0.82
method | result | size |
default | \(6 x -\frac {2 \,{\mathrm e}^{x}}{x -5}\) | \(14\) |
risch | \(6 x -\frac {2 \,{\mathrm e}^{x}}{x -5}\) | \(14\) |
norman | \(\frac {6 x^{2}-2 \,{\mathrm e}^{x}-150}{x -5}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} 6 \, x - \frac {2 \, x e^{x}}{x^{2} - 10 \, x + 25} - \frac {12 \, e^{5} E_{2}\left (-x + 5\right )}{x - 5} - 2 \, \int \frac {{\left (x + 5\right )} e^{x}}{x^{3} - 15 \, x^{2} + 75 \, x - 125}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.49, size = 13, normalized size = 0.76 \begin {gather*} 6\,x-\frac {2\,{\mathrm {e}}^x}{x-5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 10, normalized size = 0.59 \begin {gather*} 6 x - \frac {2 e^{x}}{x - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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