Optimal. Leaf size=17 \[ \frac {x}{5}+e^3 \left (x+9 x^2\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.18, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12} \begin {gather*} \frac {1}{36} e^3 (18 x+1)^2+\frac {x}{5} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (1+e^3 (5+90 x)\right ) \, dx\\ &=\frac {x}{5}+\frac {1}{36} e^3 (1+18 x)^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.12 \begin {gather*} \frac {x}{5}+e^3 x+9 e^3 x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 14, normalized size = 0.82 \begin {gather*} {\left (9 \, x^{2} + x\right )} e^{3} + \frac {1}{5} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 14, normalized size = 0.82 \begin {gather*} {\left (9 \, x^{2} + x\right )} e^{3} + \frac {1}{5} \, 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 = 0.88
method | result | size |
gosper | \(\frac {x \left (45 x \,{\mathrm e}^{3}+5 \,{\mathrm e}^{3}+1\right )}{5}\) | \(15\) |
norman | \(\left ({\mathrm e}^{3}+\frac {1}{5}\right ) x +9 x^{2} {\mathrm e}^{3}\) | \(15\) |
risch | \(9 x^{2} {\mathrm e}^{3}+x \,{\mathrm e}^{3}+\frac {x}{5}\) | \(16\) |
default | \(\frac {{\mathrm e}^{3} \left (45 x^{2}+5 x \right )}{5}+\frac {x}{5}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 14, normalized size = 0.82 \begin {gather*} {\left (9 \, x^{2} + x\right )} e^{3} + \frac {1}{5} \, 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 = 1.00 \begin {gather*} \frac {\left (90\,x+5\right )\,\left ({\mathrm {e}}^3\,\left (90\,x+5\right )+2\right )}{900} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 15, normalized size = 0.88 \begin {gather*} 9 x^{2} e^{3} + x \left (\frac {1}{5} + e^{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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