Optimal. Leaf size=35 \[ \frac {4}{\frac {5}{4}+x+4 \left (e^{e^{x^2}}+x-\frac {3}{4} \left (-x+\frac {x^2}{5}\right )\right )} \]
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Rubi [A] time = 0.26, antiderivative size = 23, normalized size of antiderivative = 0.66, number of steps used = 3, number of rules used = 3, integrand size = 71, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {6688, 12, 6686} \begin {gather*} \frac {80}{-12 x^2+80 e^{e^{x^2}}+160 x+25} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {640 \left (-20-\left (-3+20 e^{e^{x^2}+x^2}\right ) x\right )}{\left (25+80 e^{e^{x^2}}+160 x-12 x^2\right )^2} \, dx\\ &=640 \int \frac {-20-\left (-3+20 e^{e^{x^2}+x^2}\right ) x}{\left (25+80 e^{e^{x^2}}+160 x-12 x^2\right )^2} \, dx\\ &=\frac {80}{25+80 e^{e^{x^2}}+160 x-12 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 23, normalized size = 0.66 \begin {gather*} \frac {80}{25+80 e^{e^{x^2}}+160 x-12 x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 35, normalized size = 1.00 \begin {gather*} -\frac {80 \, e^{\left (x^{2}\right )}}{{\left (12 \, x^{2} - 160 \, x - 25\right )} e^{\left (x^{2}\right )} - 80 \, e^{\left (x^{2} + e^{\left (x^{2}\right )}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 21, normalized size = 0.60 \begin {gather*} -\frac {80}{12 \, x^{2} - 160 \, x - 80 \, e^{\left (e^{\left (x^{2}\right )}\right )} - 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 22, normalized size = 0.63
method | result | size |
norman | \(-\frac {80}{12 x^{2}-160 x -80 \,{\mathrm e}^{{\mathrm e}^{x^{2}}}-25}\) | \(22\) |
risch | \(-\frac {80}{12 x^{2}-160 x -80 \,{\mathrm e}^{{\mathrm e}^{x^{2}}}-25}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 21, normalized size = 0.60 \begin {gather*} -\frac {80}{12 \, x^{2} - 160 \, x - 80 \, e^{\left (e^{\left (x^{2}\right )}\right )} - 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.26, size = 21, normalized size = 0.60 \begin {gather*} \frac {80}{160\,x+80\,{\mathrm {e}}^{{\mathrm {e}}^{x^2}}-12\,x^2+25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.39, size = 19, normalized size = 0.54 \begin {gather*} \frac {80}{- 12 x^{2} + 160 x + 80 e^{e^{x^{2}}} + 25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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