Optimal. Leaf size=24 \[ \frac {8}{e^{e^{2-5 x} x^3}+3 (x+\log (2))} \]
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Rubi [A] time = 0.44, antiderivative size = 23, normalized size of antiderivative = 0.96, number of steps used = 2, number of rules used = 2, integrand size = 106, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6688, 6686} \begin {gather*} \frac {8}{e^{e^{2-5 x} x^3}+3 x+\log (8)} \end {gather*}
Antiderivative was successfully verified.
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Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-5 x} \left (-24 e^{5 x}+8 e^{2+e^{2-5 x} x^3} x^2 (-3+5 x)\right )}{\left (e^{e^{2-5 x} x^3}+3 x+\log (8)\right )^2} \, dx\\ &=\frac {8}{e^{e^{2-5 x} x^3}+3 x+\log (8)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.15, size = 23, normalized size = 0.96 \begin {gather*} \frac {8}{e^{e^{2-5 x} x^3}+3 x+\log (8)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 39, normalized size = 1.62 \begin {gather*} \frac {8 \, e^{\left (5 \, x\right )}}{3 \, {\left (x + \log \relax (2)\right )} e^{\left (5 \, x\right )} + e^{\left ({\left (x^{3} e^{2} + 5 \, x e^{\left (5 \, x\right )}\right )} e^{\left (-5 \, x\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.83, size = 621, normalized size = 25.88 \begin {gather*} \frac {8 \, {\left (15 \, x^{5} e^{\left (5 \, x + 2\right )} + 30 \, x^{4} e^{\left (5 \, x + 2\right )} \log \relax (2) + 15 \, x^{3} e^{\left (5 \, x + 2\right )} \log \relax (2)^{2} + 5 \, x^{4} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} - 9 \, x^{4} e^{\left (5 \, x + 2\right )} + 5 \, x^{3} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} \log \relax (2) - 18 \, x^{3} e^{\left (5 \, x + 2\right )} \log \relax (2) - 9 \, x^{2} e^{\left (5 \, x + 2\right )} \log \relax (2)^{2} - 3 \, x^{3} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} - 3 \, x^{2} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} \log \relax (2) + 3 \, x e^{\left (10 \, x\right )} + 3 \, e^{\left (10 \, x\right )} \log \relax (2) + e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 10 \, x\right )}\right )}}{45 \, x^{6} e^{\left (5 \, x + 2\right )} + 135 \, x^{5} e^{\left (5 \, x + 2\right )} \log \relax (2) + 135 \, x^{4} e^{\left (5 \, x + 2\right )} \log \relax (2)^{2} + 45 \, x^{3} e^{\left (5 \, x + 2\right )} \log \relax (2)^{3} + 30 \, x^{5} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} - 27 \, x^{5} e^{\left (5 \, x + 2\right )} + 60 \, x^{4} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} \log \relax (2) - 81 \, x^{4} e^{\left (5 \, x + 2\right )} \log \relax (2) + 30 \, x^{3} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} \log \relax (2)^{2} - 81 \, x^{3} e^{\left (5 \, x + 2\right )} \log \relax (2)^{2} - 27 \, x^{2} e^{\left (5 \, x + 2\right )} \log \relax (2)^{3} + 5 \, x^{4} e^{\left (2 \, x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} - 18 \, x^{4} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} + 5 \, x^{3} e^{\left (2 \, x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} \log \relax (2) - 36 \, x^{3} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} \log \relax (2) - 18 \, x^{2} e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} \log \relax (2)^{2} - 3 \, x^{3} e^{\left (2 \, x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} - 3 \, x^{2} e^{\left (2 \, x^{3} e^{\left (-5 \, x + 2\right )} + 5 \, x + 2\right )} \log \relax (2) + 9 \, x^{2} e^{\left (10 \, x\right )} + 18 \, x e^{\left (10 \, x\right )} \log \relax (2) + 9 \, e^{\left (10 \, x\right )} \log \relax (2)^{2} + 6 \, x e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 10 \, x\right )} + 6 \, e^{\left (x^{3} e^{\left (-5 \, x + 2\right )} + 10 \, x\right )} \log \relax (2) + e^{\left (2 \, x^{3} e^{\left (-5 \, x + 2\right )} + 10 \, x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.24, size = 24, normalized size = 1.00
method | result | size |
risch | \(\frac {8}{3 \ln \relax (2)+3 x +{\mathrm e}^{x^{3} {\mathrm e}^{-5 x +2}}}\) | \(24\) |
norman | \(\frac {8}{3 \ln \relax (2)+3 x +{\mathrm e}^{x^{3} {\mathrm e}^{2} {\mathrm e}^{-5 x}}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 23, normalized size = 0.96 \begin {gather*} \frac {8}{3 \, x + e^{\left (x^{3} e^{\left (-5 \, x + 2\right )}\right )} + 3 \, \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {24\,{\mathrm {e}}^{5\,x}+{\mathrm {e}}^{x^3\,{\mathrm {e}}^{-5\,x}\,{\mathrm {e}}^2}\,{\mathrm {e}}^2\,\left (24\,x^2-40\,x^3\right )}{{\mathrm {e}}^{5\,x}\,\left (9\,x^2+18\,\ln \relax (2)\,x+9\,{\ln \relax (2)}^2\right )+{\mathrm {e}}^{5\,x}\,{\mathrm {e}}^{2\,x^3\,{\mathrm {e}}^{-5\,x}\,{\mathrm {e}}^2}+{\mathrm {e}}^{5\,x}\,{\mathrm {e}}^{x^3\,{\mathrm {e}}^{-5\,x}\,{\mathrm {e}}^2}\,\left (6\,x+6\,\ln \relax (2)\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 22, normalized size = 0.92 \begin {gather*} \frac {8}{3 x + e^{x^{3} e^{2} e^{- 5 x}} + 3 \log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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