Optimal. Leaf size=19 \[ \frac {4 e^{5-x} \left (-3-\frac {10}{x}\right )}{x} \]
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Rubi [A] time = 0.13, antiderivative size = 25, normalized size of antiderivative = 1.32, number of steps used = 8, number of rules used = 3, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2199, 2177, 2178} \begin {gather*} -\frac {40 e^{5-x}}{x^2}-\frac {12 e^{5-x}}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2177
Rule 2178
Rule 2199
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {80 e^{5-x}}{x^3}+\frac {52 e^{5-x}}{x^2}+\frac {12 e^{5-x}}{x}\right ) \, dx\\ &=12 \int \frac {e^{5-x}}{x} \, dx+52 \int \frac {e^{5-x}}{x^2} \, dx+80 \int \frac {e^{5-x}}{x^3} \, dx\\ &=-\frac {40 e^{5-x}}{x^2}-\frac {52 e^{5-x}}{x}+12 e^5 \text {Ei}(-x)-40 \int \frac {e^{5-x}}{x^2} \, dx-52 \int \frac {e^{5-x}}{x} \, dx\\ &=-\frac {40 e^{5-x}}{x^2}-\frac {12 e^{5-x}}{x}-40 e^5 \text {Ei}(-x)+40 \int \frac {e^{5-x}}{x} \, dx\\ &=-\frac {40 e^{5-x}}{x^2}-\frac {12 e^{5-x}}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 17, normalized size = 0.89 \begin {gather*} -\frac {4 e^{5-x} (10+3 x)}{x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 16, normalized size = 0.84 \begin {gather*} -\frac {4 \, {\left (3 \, x + 10\right )} e^{\left (-x + 5\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 23, normalized size = 1.21 \begin {gather*} -\frac {4 \, {\left (3 \, x e^{\left (-x + 5\right )} + 10 \, e^{\left (-x + 5\right )}\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 17, normalized size = 0.89
method | result | size |
gosper | \(-\frac {4 \,{\mathrm e}^{5} \left (3 x +10\right ) {\mathrm e}^{-x}}{x^{2}}\) | \(17\) |
risch | \(-\frac {4 \left (3 x +10\right ) {\mathrm e}^{5-x}}{x^{2}}\) | \(17\) |
norman | \(\frac {\left (-12 x \,{\mathrm e}^{5}-40 \,{\mathrm e}^{5}\right ) {\mathrm e}^{-x}}{x^{2}}\) | \(19\) |
default | \(4 \,{\mathrm e}^{5} \left (-\frac {10 \,{\mathrm e}^{-x}}{x^{2}}-\frac {3 \,{\mathrm e}^{-x}}{x}\right )\) | \(24\) |
meijerg | \(-12 \,{\mathrm e}^{5} \expIntegralEi \left (1, x\right )+52 \,{\mathrm e}^{5} \left (-\frac {1}{x}+1+\frac {-2 x +2}{2 x}-\frac {{\mathrm e}^{-x}}{x}+\expIntegralEi \left (1, x\right )\right )+80 \,{\mathrm e}^{5} \left (-\frac {1}{2 x^{2}}+\frac {1}{x}-\frac {3}{4}+\frac {9 x^{2}-12 x +6}{12 x^{2}}-\frac {\left (-3 x +3\right ) {\mathrm e}^{-x}}{6 x^{2}}-\frac {\expIntegralEi \left (1, x\right )}{2}\right )\) | \(90\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.41, size = 23, normalized size = 1.21 \begin {gather*} 12 \, {\rm Ei}\left (-x\right ) e^{5} - 52 \, e^{5} \Gamma \left (-1, x\right ) - 80 \, e^{5} \Gamma \left (-2, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.38, size = 16, normalized size = 0.84 \begin {gather*} -\frac {4\,{\mathrm {e}}^{5-x}\,\left (3\,x+10\right )}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 19, normalized size = 1.00 \begin {gather*} \frac {\left (- 12 x e^{5} - 40 e^{5}\right ) e^{- x}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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