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, 2228}
\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 2228
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 = 0.10, 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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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(79\) vs.
\(2(19)=38\).
time = 0.65, size = 80, normalized size = 3.64
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] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.30, 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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Fricas [A]
time = 0.36, 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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Sympy [A]
time = 0.04, 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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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 72 vs.
\(2 (19) = 38\).
time = 0.41, size = 72, normalized size = 3.27 \begin {gather*} -\frac {5 \, {\left (x + 23\right )}^{9} - 1035 \, {\left (x + 23\right )}^{8} + 95220 \, {\left (x + 23\right )}^{7} - 5110140 \, {\left (x + 23\right )}^{6} + 176299830 \, {\left (x + 23\right )}^{5} - 4054896090 \, {\left (x + 23\right )}^{4} + 62175073380 \, {\left (x + 23\right )}^{3} - 612868580465 \, {\left (x + 23\right )}^{2} + 3132439411355 \, x + e^{\left (-x - 23\right )} + 72046106461165}{5 \, 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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