Optimal. Leaf size=20 \[ 4+\left (3+e^x+x\right )^2-4 \left (10+x-16 x^4\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 30, normalized size of antiderivative = 1.50, 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 = {2194, 2176} \begin {gather*} 64 x^4+x^2+2 x-2 e^x+e^{2 x}+2 e^x (x+4) \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 x+x^2+64 x^4+2 \int e^{2 x} \, dx+\int e^x (8+2 x) \, dx\\ &=e^{2 x}+2 x+x^2+64 x^4+2 e^x (4+x)-2 \int e^x \, dx\\ &=-2 e^x+e^{2 x}+2 x+x^2+64 x^4+2 e^x (4+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 32, normalized size = 1.60 \begin {gather*} 2 \left (\frac {e^{2 x}}{2}+x+\frac {x^2}{2}+32 x^4+e^x (3+x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 23, normalized size = 1.15 \begin {gather*} 64 \, x^{4} + x^{2} + 2 \, {\left (x + 3\right )} e^{x} + 2 \, x + e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 23, normalized size = 1.15 \begin {gather*} 64 \, x^{4} + x^{2} + 2 \, {\left (x + 3\right )} e^{x} + 2 \, x + e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 25, normalized size = 1.25
method | result | size |
risch | \({\mathrm e}^{2 x}+\left (2 x +6\right ) {\mathrm e}^{x}+64 x^{4}+x^{2}+2 x\) | \(25\) |
default | \(2 x +2 \,{\mathrm e}^{x} x +6 \,{\mathrm e}^{x}+x^{2}+64 x^{4}+{\mathrm e}^{2 x}\) | \(26\) |
norman | \(2 x +2 \,{\mathrm e}^{x} x +6 \,{\mathrm e}^{x}+x^{2}+64 x^{4}+{\mathrm e}^{2 x}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 23, normalized size = 1.15 \begin {gather*} 64 \, x^{4} + x^{2} + 2 \, {\left (x + 3\right )} e^{x} + 2 \, x + e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.13, size = 25, normalized size = 1.25 \begin {gather*} 2\,x+{\mathrm {e}}^{2\,x}+6\,{\mathrm {e}}^x+2\,x\,{\mathrm {e}}^x+x^2+64\,x^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 24, normalized size = 1.20 \begin {gather*} 64 x^{4} + x^{2} + 2 x + \left (2 x + 6\right ) e^{x} + e^{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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