Optimal. Leaf size=29 \[ e^5+x-2 e^{8 x} \left (-4-\frac {e^{2 x}}{2}-x+x^2\right ) \]
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Rubi [A] time = 0.16, antiderivative size = 32, normalized size of antiderivative = 1.10, number of steps used = 12, number of rules used = 5, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {6741, 12, 6742, 2194, 2176} \begin {gather*} -2 e^{8 x} x^2+2 e^{8 x} x+x+8 e^{8 x}+e^{10 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2176
Rule 2194
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+\int e^{8 x} \left (66+10 e^{2 x}+12 x-16 x^2\right ) \, dx\\ &=x+\int 2 e^{8 x} \left (33+5 e^{2 x}+6 x-8 x^2\right ) \, dx\\ &=x+2 \int e^{8 x} \left (33+5 e^{2 x}+6 x-8 x^2\right ) \, dx\\ &=x+2 \int \left (33 e^{8 x}+5 e^{10 x}+6 e^{8 x} x-8 e^{8 x} x^2\right ) \, dx\\ &=x+10 \int e^{10 x} \, dx+12 \int e^{8 x} x \, dx-16 \int e^{8 x} x^2 \, dx+66 \int e^{8 x} \, dx\\ &=\frac {33 e^{8 x}}{4}+e^{10 x}+x+\frac {3}{2} e^{8 x} x-2 e^{8 x} x^2-\frac {3}{2} \int e^{8 x} \, dx+4 \int e^{8 x} x \, dx\\ &=\frac {129 e^{8 x}}{16}+e^{10 x}+x+2 e^{8 x} x-2 e^{8 x} x^2-\frac {1}{2} \int e^{8 x} \, dx\\ &=8 e^{8 x}+e^{10 x}+x+2 e^{8 x} x-2 e^{8 x} x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 22, normalized size = 0.76 \begin {gather*} e^{10 x}+x+2 e^{8 x} \left (4+x-x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 20, normalized size = 0.69 \begin {gather*} -2 \, {\left (x^{2} - x - 4\right )} e^{\left (8 \, x\right )} + x + e^{\left (10 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 20, normalized size = 0.69 \begin {gather*} -2 \, {\left (x^{2} - x - 4\right )} e^{\left (8 \, x\right )} + x + e^{\left (10 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 22, normalized size = 0.76
method | result | size |
risch | \({\mathrm e}^{10 x}+\left (-2 x^{2}+2 x +8\right ) {\mathrm e}^{8 x}+x\) | \(22\) |
default | \(x +8 \,{\mathrm e}^{8 x}+{\mathrm e}^{10 x}+2 x \,{\mathrm e}^{8 x}-2 \,{\mathrm e}^{8 x} x^{2}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 39, normalized size = 1.34 \begin {gather*} -\frac {1}{16} \, {\left (32 \, x^{2} - 8 \, x + 1\right )} e^{\left (8 \, x\right )} + \frac {3}{16} \, {\left (8 \, x - 1\right )} e^{\left (8 \, x\right )} + x + e^{\left (10 \, x\right )} + \frac {33}{4} \, e^{\left (8 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.39, size = 28, normalized size = 0.97 \begin {gather*} x+8\,{\mathrm {e}}^{8\,x}+{\mathrm {e}}^{10\,x}+2\,x\,{\mathrm {e}}^{8\,x}-2\,x^2\,{\mathrm {e}}^{8\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 20, normalized size = 0.69 \begin {gather*} x + \left (- 2 x^{2} + 2 x + 8\right ) e^{8 x} + e^{10 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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