Optimal. Leaf size=24 \[ 2+e^{6-x+\frac {\left (4+3 x^3\right )^2}{x}} x \]
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Rubi [B] time = 0.13, antiderivative size = 94, normalized size of antiderivative = 3.92, number of steps used = 1, number of rules used = 1, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {2288} \begin {gather*} -\frac {e^{\frac {9 x^6+24 x^3-x^2+6 x+16}{x}} \left (-45 x^6-48 x^3+x^2+16\right )}{x \left (\frac {2 \left (27 x^5+36 x^2-x+3\right )}{x}-\frac {9 x^6+24 x^3-x^2+6 x+16}{x^2}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {e^{\frac {16+6 x-x^2+24 x^3+9 x^6}{x}} \left (16+x^2-48 x^3-45 x^6\right )}{x \left (\frac {2 \left (3-x+36 x^2+27 x^5\right )}{x}-\frac {16+6 x-x^2+24 x^3+9 x^6}{x^2}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 24, normalized size = 1.00 \begin {gather*} e^{6+\frac {16}{x}-x+24 x^2+9 x^5} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 27, normalized size = 1.12 \begin {gather*} x e^{\left (\frac {9 \, x^{6} + 24 \, x^{3} - x^{2} + 6 \, x + 16}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 27, normalized size = 1.12 \begin {gather*} x e^{\left (\frac {9 \, x^{6} + 24 \, x^{3} - x^{2} + 6 \, x + 16}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 28, normalized size = 1.17
method | result | size |
gosper | \(x \,{\mathrm e}^{\frac {9 x^{6}+24 x^{3}-x^{2}+6 x +16}{x}}\) | \(28\) |
norman | \(x \,{\mathrm e}^{\frac {9 x^{6}+24 x^{3}-x^{2}+6 x +16}{x}}\) | \(28\) |
risch | \(x \,{\mathrm e}^{\frac {9 x^{6}+24 x^{3}-x^{2}+6 x +16}{x}}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 23, normalized size = 0.96 \begin {gather*} x e^{\left (9 \, x^{5} + 24 \, x^{2} - x + \frac {16}{x} + 6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.27, size = 26, normalized size = 1.08 \begin {gather*} x\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^6\,{\mathrm {e}}^{9\,x^5}\,{\mathrm {e}}^{16/x}\,{\mathrm {e}}^{24\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 22, normalized size = 0.92 \begin {gather*} x e^{\frac {9 x^{6} + 24 x^{3} - x^{2} + 6 x + 16}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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