Optimal. Leaf size=27 \[ 5 \left (2+e^{\frac {\left (x+x^2\right )^2}{x}}+\frac {6-x}{5}\right ) x \]
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Rubi [A] time = 0.04, antiderivative size = 47, normalized size of antiderivative = 1.74, number of steps used = 2, number of rules used = 1, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.030, Rules used = {2288} \begin {gather*} -x^2+\frac {5 e^{x^3+2 x^2+x} \left (3 x^3+4 x^2+x\right )}{3 x^2+4 x+1}+16 x \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=16 x-x^2+\int e^{x+2 x^2+x^3} \left (5+5 x+20 x^2+15 x^3\right ) \, dx\\ &=16 x-x^2+\frac {5 e^{x+2 x^2+x^3} \left (x+4 x^2+3 x^3\right )}{1+4 x+3 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 17, normalized size = 0.63 \begin {gather*} -x \left (-16-5 e^{x (1+x)^2}+x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 23, normalized size = 0.85 \begin {gather*} -x^{2} + 5 \, x e^{\left (x^{3} + 2 \, x^{2} + x\right )} + 16 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 23, normalized size = 0.85 \begin {gather*} -x^{2} + 5 \, x e^{\left (x^{3} + 2 \, x^{2} + x\right )} + 16 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 21, normalized size = 0.78
method | result | size |
risch | \(16 x +5 \,{\mathrm e}^{x \left (x +1\right )^{2}} x -x^{2}\) | \(21\) |
default | \(16 x +5 \,{\mathrm e}^{x^{3}+2 x^{2}+x} x -x^{2}\) | \(24\) |
norman | \(16 x +5 \,{\mathrm e}^{x^{3}+2 x^{2}+x} x -x^{2}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 23, normalized size = 0.85 \begin {gather*} -x^{2} + 5 \, x e^{\left (x^{3} + 2 \, x^{2} + x\right )} + 16 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 24, normalized size = 0.89 \begin {gather*} 16\,x-x^2+5\,x\,{\mathrm {e}}^{x^3}\,{\mathrm {e}}^{2\,x^2}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 20, normalized size = 0.74 \begin {gather*} - x^{2} + 5 x e^{x^{3} + 2 x^{2} + x} + 16 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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