Optimal. Leaf size=13 \[ x \left (6+e \left (\frac {19}{5}+2 x\right )\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.23, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12} \begin {gather*} \frac {1}{200} e (20 x+19)^2+6 x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int (30+e (19+20 x)) \, dx\\ &=6 x+\frac {1}{200} e (19+20 x)^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.23 \begin {gather*} 6 x+\frac {19 e x}{5}+2 e x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 17, normalized size = 1.31 \begin {gather*} \frac {1}{5} \, {\left (10 \, x^{2} + 19 \, x\right )} e + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 17, normalized size = 1.31 \begin {gather*} \frac {1}{5} \, {\left (10 \, x^{2} + 19 \, x\right )} e + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 15, normalized size = 1.15
method | result | size |
gosper | \(\frac {x \left (10 x \,{\mathrm e}+19 \,{\mathrm e}+30\right )}{5}\) | \(15\) |
norman | \(\left (\frac {19 \,{\mathrm e}}{5}+6\right ) x +2 x^{2} {\mathrm e}\) | \(17\) |
risch | \(2 x^{2} {\mathrm e}+\frac {19 x \,{\mathrm e}}{5}+6 x\) | \(17\) |
default | \(\frac {{\mathrm e} \left (10 x^{2}+19 x \right )}{5}+6 x\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 17, normalized size = 1.31 \begin {gather*} \frac {1}{5} \, {\left (10 \, x^{2} + 19 \, x\right )} e + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 17, normalized size = 1.31 \begin {gather*} \frac {\left (20\,x+19\right )\,\left (\mathrm {e}\,\left (20\,x+19\right )+60\right )}{200} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 17, normalized size = 1.31 \begin {gather*} 2 e x^{2} + x \left (6 + \frac {19 e}{5}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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