Optimal. Leaf size=32 \[ x^2 \left (3+\frac {1}{3} \left (e^{-\frac {2}{x}+\frac {x}{5}}+\frac {5}{x}\right ) x^2\right ) \]
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Rubi [A] time = 0.11, antiderivative size = 56, normalized size of antiderivative = 1.75, number of steps used = 4, number of rules used = 3, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {12, 1594, 2288} \begin {gather*} \frac {5 x^3}{3}+\frac {e^{-\frac {10-x^2}{5 x}} \left (x^2+10\right ) x^2}{3 \left (\frac {10-x^2}{x^2}+2\right )}+3 x^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 1594
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{15} \int \left (90 x+75 x^2+e^{\frac {-10+x^2}{5 x}} \left (10 x^2+20 x^3+x^4\right )\right ) \, dx\\ &=3 x^2+\frac {5 x^3}{3}+\frac {1}{15} \int e^{\frac {-10+x^2}{5 x}} \left (10 x^2+20 x^3+x^4\right ) \, dx\\ &=3 x^2+\frac {5 x^3}{3}+\frac {1}{15} \int e^{\frac {-10+x^2}{5 x}} x^2 \left (10+20 x+x^2\right ) \, dx\\ &=3 x^2+\frac {5 x^3}{3}+\frac {e^{-\frac {10-x^2}{5 x}} x^2 \left (10+x^2\right )}{3 \left (2+\frac {10-x^2}{x^2}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 29, normalized size = 0.91 \begin {gather*} \frac {1}{3} x^2 \left (9+5 x+e^{-\frac {2}{x}+\frac {x}{5}} x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 27, normalized size = 0.84 \begin {gather*} \frac {1}{3} \, x^{4} e^{\left (\frac {x^{2} - 10}{5 \, x}\right )} + \frac {5}{3} \, x^{3} + 3 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 27, normalized size = 0.84 \begin {gather*} \frac {1}{3} \, x^{4} e^{\left (\frac {x^{2} - 10}{5 \, x}\right )} + \frac {5}{3} \, x^{3} + 3 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 28, normalized size = 0.88
method | result | size |
default | \(3 x^{2}+\frac {5 x^{3}}{3}+\frac {{\mathrm e}^{\frac {x^{2}-10}{5 x}} x^{4}}{3}\) | \(28\) |
norman | \(3 x^{2}+\frac {5 x^{3}}{3}+\frac {{\mathrm e}^{\frac {x^{2}-10}{5 x}} x^{4}}{3}\) | \(28\) |
risch | \(3 x^{2}+\frac {5 x^{3}}{3}+\frac {{\mathrm e}^{\frac {x^{2}-10}{5 x}} x^{4}}{3}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 26, normalized size = 0.81 \begin {gather*} \frac {1}{3} \, x^{4} e^{\left (\frac {1}{5} \, x - \frac {2}{x}\right )} + \frac {5}{3} \, x^{3} + 3 \, x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.21, size = 26, normalized size = 0.81 \begin {gather*} \frac {x^4\,{\mathrm {e}}^{\frac {x}{5}-\frac {2}{x}}}{3}+3\,x^2+\frac {5\,x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 26, normalized size = 0.81 \begin {gather*} \frac {x^{4} e^{\frac {\frac {x^{2}}{5} - 2}{x}}}{3} + \frac {5 x^{3}}{3} + 3 x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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