Optimal. Leaf size=23 \[ -\frac {e^x}{14 x^2}-x+e^{5-x} x \]
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Rubi [A] time = 0.06, antiderivative size = 35, normalized size of antiderivative = 1.52, number of steps used = 6, number of rules used = 5, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.122, Rules used = {12, 14, 2176, 2194, 2197} \begin {gather*} -\frac {e^x}{14 x^2}-e^{5-x} (1-x)+e^{5-x}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2176
Rule 2194
Rule 2197
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{14} \int \frac {e^x (2-x)-14 x^3+e^{5-x} \left (14 x^3-14 x^4\right )}{x^3} \, dx\\ &=\frac {1}{14} \int \left (-14-14 e^{5-x} (-1+x)-\frac {e^x (-2+x)}{x^3}\right ) \, dx\\ &=-x-\frac {1}{14} \int \frac {e^x (-2+x)}{x^3} \, dx-\int e^{5-x} (-1+x) \, dx\\ &=-e^{5-x} (1-x)-\frac {e^x}{14 x^2}-x-\int e^{5-x} \, dx\\ &=e^{5-x}-e^{5-x} (1-x)-\frac {e^x}{14 x^2}-x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 23, normalized size = 1.00 \begin {gather*} -\frac {e^x}{14 x^2}-x+e^{5-x} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 30, normalized size = 1.30 \begin {gather*} \frac {{\left (14 \, x^{3} e^{5} - 14 \, x^{3} e^{x} - e^{\left (2 \, x\right )}\right )} e^{\left (-x\right )}}{14 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 26, normalized size = 1.13 \begin {gather*} \frac {14 \, x^{3} e^{\left (-x + 5\right )} - 14 \, x^{3} - e^{x}}{14 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 20, normalized size = 0.87
method | result | size |
risch | \(x \,{\mathrm e}^{5-x}-x -\frac {{\mathrm e}^{x}}{14 x^{2}}\) | \(20\) |
norman | \(\frac {\left (x^{3} {\mathrm e}^{5}-\frac {{\mathrm e}^{2 x}}{14}-{\mathrm e}^{x} x^{3}\right ) {\mathrm e}^{-x}}{x^{2}}\) | \(29\) |
default | \(-x -{\mathrm e}^{5} {\mathrm e}^{-x}-\frac {{\mathrm e}^{x}}{14 x^{2}}-{\mathrm e}^{5} \left (-x \,{\mathrm e}^{-x}-{\mathrm e}^{-x}\right )\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.38, size = 38, normalized size = 1.65 \begin {gather*} {\left (x e^{5} + e^{5}\right )} e^{\left (-x\right )} - x - e^{\left (-x + 5\right )} - \frac {1}{14} \, \Gamma \left (-1, -x\right ) - \frac {1}{7} \, \Gamma \left (-2, -x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.17, size = 18, normalized size = 0.78 \begin {gather*} x\,\left ({\mathrm {e}}^{5-x}-1\right )-\frac {{\mathrm {e}}^x}{14\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 20, normalized size = 0.87 \begin {gather*} - x + \frac {14 x^{3} e^{5} e^{- x} - e^{x}}{14 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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