Optimal. Leaf size=26 \[ 4 \left (-5+\left (-4+e^x\right )^2+\frac {2 x}{5}+\frac {1}{2} x \left (x+x^2\right )\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.08, number of steps used = 4, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 2194} \begin {gather*} 2 x^3+2 x^2+\frac {8 x}{5}-32 e^x+4 e^{2 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (8-160 e^x+40 e^{2 x}+20 x+30 x^2\right ) \, dx\\ &=\frac {8 x}{5}+2 x^2+2 x^3+8 \int e^{2 x} \, dx-32 \int e^x \, dx\\ &=-32 e^x+4 e^{2 x}+\frac {8 x}{5}+2 x^2+2 x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 1.08 \begin {gather*} -32 e^x+4 e^{2 x}+\frac {8 x}{5}+2 x^2+2 x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.78, size = 24, normalized size = 0.92 \begin {gather*} 2 \, x^{3} + 2 \, x^{2} + \frac {8}{5} \, x + 4 \, e^{\left (2 \, x\right )} - 32 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 24, normalized size = 0.92 \begin {gather*} 2 \, x^{3} + 2 \, x^{2} + \frac {8}{5} \, x + 4 \, e^{\left (2 \, x\right )} - 32 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 25, normalized size = 0.96
method | result | size |
default | \(\frac {8 x}{5}+2 x^{2}+2 x^{3}+4 \,{\mathrm e}^{2 x}-32 \,{\mathrm e}^{x}\) | \(25\) |
norman | \(\frac {8 x}{5}+2 x^{2}+2 x^{3}+4 \,{\mathrm e}^{2 x}-32 \,{\mathrm e}^{x}\) | \(25\) |
risch | \(\frac {8 x}{5}+2 x^{2}+2 x^{3}+4 \,{\mathrm e}^{2 x}-32 \,{\mathrm e}^{x}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.69, size = 24, normalized size = 0.92 \begin {gather*} 2 \, x^{3} + 2 \, x^{2} + \frac {8}{5} \, x + 4 \, e^{\left (2 \, x\right )} - 32 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.13, size = 24, normalized size = 0.92 \begin {gather*} \frac {8\,x}{5}+4\,{\mathrm {e}}^{2\,x}-32\,{\mathrm {e}}^x+2\,x^2+2\,x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 26, normalized size = 1.00 \begin {gather*} 2 x^{3} + 2 x^{2} + \frac {8 x}{5} + 4 e^{2 x} - 32 e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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