Optimal. Leaf size=25 \[ 1+e^{\left (4+e^x+\frac {10}{x^2}+x-x (4+x)\right )^2} x \]
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Rubi [B] time = 29.82, antiderivative size = 330, normalized size of antiderivative = 13.20, number of steps used = 1, number of rules used = 1, integrand size = 152, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.007, Rules used = {2288} \begin {gather*} -\frac {\left (-2 x^8-9 x^7-x^6-e^{2 x} x^5+12 x^5-30 x^3+80 x^2+e^x \left (x^7+5 x^6-x^5-10 x^3+20 x^2\right )+200\right ) \exp \left (\frac {x^8+6 x^7+x^6-24 x^5+e^{2 x} x^4-4 x^4-60 x^3+80 x^2+2 e^x \left (-x^6-3 x^5+4 x^4+10 x^2\right )+100}{x^4}\right )}{x^4 \left (\frac {4 x^7+21 x^6+3 x^5+e^{2 x} x^4-60 x^4+2 e^{2 x} x^3-8 x^3-90 x^2+e^x \left (-6 x^5-15 x^4+16 x^3+20 x\right )+e^x \left (-x^6-3 x^5+4 x^4+10 x^2\right )+80 x}{x^4}-\frac {2 \left (x^8+6 x^7+x^6-24 x^5+e^{2 x} x^4-4 x^4-60 x^3+80 x^2+2 e^x \left (-x^6-3 x^5+4 x^4+10 x^2\right )+100\right )}{x^5}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {\exp \left (\frac {100+80 x^2-60 x^3-4 x^4+e^{2 x} x^4-24 x^5+x^6+6 x^7+x^8+2 e^x \left (10 x^2+4 x^4-3 x^5-x^6\right )}{x^4}\right ) \left (200+80 x^2-30 x^3+12 x^5-e^{2 x} x^5-x^6-9 x^7-2 x^8+e^x \left (20 x^2-10 x^3-x^5+5 x^6+x^7\right )\right )}{x^4 \left (\frac {80 x-90 x^2-8 x^3+2 e^{2 x} x^3-60 x^4+e^{2 x} x^4+3 x^5+21 x^6+4 x^7+e^x \left (20 x+16 x^3-15 x^4-6 x^5\right )+e^x \left (10 x^2+4 x^4-3 x^5-x^6\right )}{x^4}-\frac {2 \left (100+80 x^2-60 x^3-4 x^4+e^{2 x} x^4-24 x^5+x^6+6 x^7+x^8+2 e^x \left (10 x^2+4 x^4-3 x^5-x^6\right )\right )}{x^5}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.17, size = 30, normalized size = 1.20 \begin {gather*} e^{\frac {\left (-10-\left (4+e^x\right ) x^2+3 x^3+x^4\right )^2}{x^4}} x \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.58, size = 71, normalized size = 2.84 \begin {gather*} x e^{\left (\frac {x^{8} + 6 \, x^{7} + x^{6} - 24 \, x^{5} + x^{4} e^{\left (2 \, x\right )} - 4 \, x^{4} - 60 \, x^{3} + 80 \, x^{2} - 2 \, {\left (x^{6} + 3 \, x^{5} - 4 \, x^{4} - 10 \, x^{2}\right )} e^{x} + 100}{x^{4}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (4 \, x^{8} + 18 \, x^{7} + 2 \, x^{6} + 2 \, x^{5} e^{\left (2 \, x\right )} - 24 \, x^{5} + x^{4} + 60 \, x^{3} - 160 \, x^{2} - 2 \, {\left (x^{7} + 5 \, x^{6} - x^{5} - 10 \, x^{3} + 20 \, x^{2}\right )} e^{x} - 400\right )} e^{\left (\frac {x^{8} + 6 \, x^{7} + x^{6} - 24 \, x^{5} + x^{4} e^{\left (2 \, x\right )} - 4 \, x^{4} - 60 \, x^{3} + 80 \, x^{2} - 2 \, {\left (x^{6} + 3 \, x^{5} - 4 \, x^{4} - 10 \, x^{2}\right )} e^{x} + 100}{x^{4}}\right )}}{x^{4}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.31, size = 83, normalized size = 3.32
method | result | size |
risch | \(x \,{\mathrm e}^{-\frac {-x^{8}+2 x^{6} {\mathrm e}^{x}-6 x^{7}+6 x^{5} {\mathrm e}^{x}-x^{6}-8 \,{\mathrm e}^{x} x^{4}-{\mathrm e}^{2 x} x^{4}+24 x^{5}+4 x^{4}-20 \,{\mathrm e}^{x} x^{2}+60 x^{3}-80 x^{2}-100}{x^{4}}}\) | \(83\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.65, size = 61, normalized size = 2.44 \begin {gather*} x e^{\left (x^{4} + 6 \, x^{3} - 2 \, x^{2} e^{x} + x^{2} - 6 \, x e^{x} - 24 \, x - \frac {60}{x} + \frac {20 \, e^{x}}{x^{2}} + \frac {80}{x^{2}} + \frac {100}{x^{4}} + e^{\left (2 \, x\right )} + 8 \, e^{x} - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.55, size = 72, normalized size = 2.88 \begin {gather*} x\,{\mathrm {e}}^{-6\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-24\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{-4}\,{\mathrm {e}}^{-2\,x^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{\frac {20\,{\mathrm {e}}^x}{x^2}}\,{\mathrm {e}}^{6\,x^3}\,{\mathrm {e}}^{-\frac {60}{x}}\,{\mathrm {e}}^{\frac {80}{x^2}}\,{\mathrm {e}}^{\frac {100}{x^4}}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{8\,{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 4.07, size = 71, normalized size = 2.84 \begin {gather*} x e^{\frac {x^{8} + 6 x^{7} + x^{6} - 24 x^{5} + x^{4} e^{2 x} - 4 x^{4} - 60 x^{3} + 80 x^{2} + \left (- 2 x^{6} - 6 x^{5} + 8 x^{4} + 20 x^{2}\right ) e^{x} + 100}{x^{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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