Optimal. Leaf size=20 \[ \frac {e^x}{x^2 \left (-2+x^5\right )^2+\log (4)} \]
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Rubi [B] time = 0.97, antiderivative size = 68, normalized size of antiderivative = 3.40, number of steps used = 1, number of rules used = 1, integrand size = 82, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {2288} \begin {gather*} \frac {e^x \left (x^{12}-4 x^7+4 x^2+\log (4)\right )}{x^{24}-8 x^{19}+24 x^{14}-32 x^9+16 x^4+2 \left (x^{12}-4 x^7+4 x^2\right ) \log (4)+\log ^2(4)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^x \left (4 x^2-4 x^7+x^{12}+\log (4)\right )}{16 x^4-32 x^9+24 x^{14}-8 x^{19}+x^{24}+2 \left (4 x^2-4 x^7+x^{12}\right ) \log (4)+\log ^2(4)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.01, size = 22, normalized size = 1.10 \begin {gather*} \frac {e^x}{4 x^2-4 x^7+x^{12}+\log (4)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 23, normalized size = 1.15 \begin {gather*} \frac {e^{x}}{x^{12} - 4 \, x^{7} + 4 \, x^{2} + 2 \, \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.88, size = 23, normalized size = 1.15 \begin {gather*} \frac {e^{x}}{x^{12} - 4 \, x^{7} + 4 \, x^{2} + 2 \, \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.42, size = 24, normalized size = 1.20
method | result | size |
gosper | \(\frac {{\mathrm e}^{x}}{x^{12}-4 x^{7}+4 x^{2}+2 \ln \relax (2)}\) | \(24\) |
risch | \(\frac {{\mathrm e}^{x}}{x^{12}-4 x^{7}+4 x^{2}+2 \ln \relax (2)}\) | \(24\) |
default | \(\text {Expression too large to display}\) | \(3222\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 23, normalized size = 1.15 \begin {gather*} \frac {e^{x}}{x^{12} - 4 \, x^{7} + 4 \, x^{2} + 2 \, \log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.61, size = 21, normalized size = 1.05 \begin {gather*} \frac {{\mathrm {e}}^x}{x^{12}-4\,x^7+4\,x^2+\ln \relax (4)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 20, normalized size = 1.00 \begin {gather*} \frac {e^{x}}{x^{12} - 4 x^{7} + 4 x^{2} + 2 \log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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