Optimal. Leaf size=22 \[ 3-\frac {e^{-23-x}}{5 x}+x-x^8 \]
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Rubi [A] time = 0.05, antiderivative size = 21, normalized size of antiderivative = 0.95, number of steps used = 5, number of rules used = 3, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {12, 14, 2197} \begin {gather*} -x^8+x-\frac {e^{-x-23}}{5 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2197
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \frac {5 x^2-40 x^9+e^{-23-x} (1+x)}{x^2} \, dx\\ &=\frac {1}{5} \int \left (\frac {e^{-23-x} (1+x)}{x^2}-5 \left (-1+8 x^7\right )\right ) \, dx\\ &=\frac {1}{5} \int \frac {e^{-23-x} (1+x)}{x^2} \, dx-\int \left (-1+8 x^7\right ) \, dx\\ &=-\frac {e^{-23-x}}{5 x}+x-x^8\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 21, normalized size = 0.95 \begin {gather*} -\frac {e^{-23-x}}{5 x}+x-x^8 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 22, normalized size = 1.00 \begin {gather*} -\frac {5 \, x^{9} - 5 \, x^{2} + e^{\left (-x - 23\right )}}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 26, normalized size = 1.18 \begin {gather*} -\frac {{\left (5 \, x^{9} e^{23} - 5 \, x^{2} e^{23} + e^{\left (-x\right )}\right )} e^{\left (-23\right )}}{5 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 19, normalized size = 0.86
method | result | size |
risch | \(-x^{8}+x -\frac {{\mathrm e}^{-x -23}}{5 x}\) | \(19\) |
norman | \(\frac {x^{2}-x^{9}-\frac {{\mathrm e}^{-x -23}}{5}}{x}\) | \(22\) |
derivativedivides | \(27238603577 x +626487882271-360435208 \left (-x -23\right )^{3}-19588870 \left (-x -23\right )^{4}-681352 \left (-x -23\right )^{5}-14812 \left (-x -23\right )^{6}-184 \left (-x -23\right )^{7}-\left (-x -23\right )^{8}-4145004892 \left (-x -23\right )^{2}-\frac {{\mathrm e}^{-x -23}}{5 x}\) | \(80\) |
default | \(27238603577 x +626487882271-360435208 \left (-x -23\right )^{3}-19588870 \left (-x -23\right )^{4}-681352 \left (-x -23\right )^{5}-14812 \left (-x -23\right )^{6}-184 \left (-x -23\right )^{7}-\left (-x -23\right )^{8}-4145004892 \left (-x -23\right )^{2}-\frac {{\mathrm e}^{-x -23}}{5 x}\) | \(80\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.37, size = 22, normalized size = 1.00 \begin {gather*} -x^{8} + \frac {1}{5} \, {\rm Ei}\left (-x\right ) e^{\left (-23\right )} - \frac {1}{5} \, e^{\left (-23\right )} \Gamma \left (-1, x\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.13, size = 18, normalized size = 0.82 \begin {gather*} x-\frac {{\mathrm {e}}^{-x-23}}{5\,x}-x^8 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 14, normalized size = 0.64 \begin {gather*} - x^{8} + x - \frac {e^{- x - 23}}{5 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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