Optimal. Leaf size=22 \[ x-e^{e^{12}+\frac {17+x}{x}} (5+x)^2 \]
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Rubi [A] time = 0.10, antiderivative size = 21, normalized size of antiderivative = 0.95, number of steps used = 3, number of rules used = 2, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.054, Rules used = {14, 2288} \begin {gather*} x-e^{\frac {17}{x}+e^{12}+1} (x+5)^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-\frac {e^{1+e^{12}+\frac {17}{x}} (5+x) \left (-85-17 x+2 x^2\right )}{x^2}\right ) \, dx\\ &=x-\int \frac {e^{1+e^{12}+\frac {17}{x}} (5+x) \left (-85-17 x+2 x^2\right )}{x^2} \, dx\\ &=x-e^{1+e^{12}+\frac {17}{x}} (5+x)^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 21, normalized size = 0.95 \begin {gather*} x-e^{1+e^{12}+\frac {17}{x}} (5+x)^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 24, normalized size = 1.09 \begin {gather*} -{\left (x^{2} + 10 \, x + 25\right )} e^{\left (\frac {x e^{12} + x + 17}{x}\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 2.53, size = 48, normalized size = 2.18 \begin {gather*} -x^{2} e^{\left (\frac {x e^{12} + x + 17}{x}\right )} - 10 \, x e^{\left (\frac {x e^{12} + x + 17}{x}\right )} + x - 25 \, e^{\left (\frac {x e^{12} + x + 17}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 32, normalized size = 1.45
method | result | size |
risch | \(x +\left (-{\mathrm e}^{{\mathrm e}^{12}} x^{2}-10 \,{\mathrm e}^{{\mathrm e}^{12}} x -25 \,{\mathrm e}^{{\mathrm e}^{12}}\right ) {\mathrm e}^{\frac {x +17}{x}}\) | \(32\) |
derivativedivides | \(x -{\mathrm e}^{{\mathrm e}^{12}} \left ({\mathrm e}^{1+\frac {17}{x}} x^{2}+10 \,{\mathrm e}^{1+\frac {17}{x}} x +25 \,{\mathrm e}^{1+\frac {17}{x}}\right )\) | \(42\) |
default | \(x -{\mathrm e}^{{\mathrm e}^{12}} \left ({\mathrm e}^{1+\frac {17}{x}} x^{2}+10 \,{\mathrm e}^{1+\frac {17}{x}} x +25 \,{\mathrm e}^{1+\frac {17}{x}}\right )\) | \(42\) |
norman | \(\frac {x^{2}-25 \,{\mathrm e}^{\frac {x +17}{x}} {\mathrm e}^{{\mathrm e}^{12}} x -10 \,{\mathrm e}^{\frac {x +17}{x}} {\mathrm e}^{{\mathrm e}^{12}} x^{2}-{\mathrm e}^{\frac {x +17}{x}} {\mathrm e}^{{\mathrm e}^{12}} x^{3}}{x}\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.57, size = 82, normalized size = 3.73 \begin {gather*} -170 \, {\rm Ei}\left (\frac {17}{x}\right ) e^{\left ({\left (e^{8} - e^{4} + 1\right )} {\left (e^{4} + 1\right )}\right )} - 119 \, e^{\left ({\left (e^{8} - e^{4} + 1\right )} {\left (e^{4} + 1\right )}\right )} \Gamma \left (-1, -\frac {17}{x}\right ) - 578 \, e^{\left ({\left (e^{8} - e^{4} + 1\right )} {\left (e^{4} + 1\right )}\right )} \Gamma \left (-2, -\frac {17}{x}\right ) + x - 25 \, e^{\left (\frac {17}{x} + e^{12} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.19, size = 42, normalized size = 1.91 \begin {gather*} x-25\,{\mathrm {e}}^{{\mathrm {e}}^{12}+\frac {17}{x}+1}-10\,x\,{\mathrm {e}}^{{\mathrm {e}}^{12}+\frac {17}{x}+1}-x^2\,{\mathrm {e}}^{{\mathrm {e}}^{12}+\frac {17}{x}+1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 32, normalized size = 1.45 \begin {gather*} x + \left (- x^{2} e^{e^{12}} - 10 x e^{e^{12}} - 25 e^{e^{12}}\right ) e^{\frac {x + 17}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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