Optimal. Leaf size=15 \[ \frac {11}{4} x \left (\frac {3}{4}+2 e^4+x\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.33, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {12}
\begin {gather*} \frac {11}{256} (8 x+3)^2+\frac {11 e^4 x}{2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (88 e^5+e (33+88 x)\right ) \, dx}{16 e}\\ &=\frac {11 e^4 x}{2}+\frac {11}{256} (3+8 x)^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 19, normalized size = 1.27 \begin {gather*} \frac {11}{16} \left (3 x+8 e^4 x+4 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.22, size = 25, normalized size = 1.67
method | result | size |
risch | \(\frac {11 x \,{\mathrm e}^{4}}{2}+\frac {11 x^{2}}{4}+\frac {33 x}{16}\) | \(15\) |
gosper | \(\frac {11 x \left (4 x \,{\mathrm e}+8 \,{\mathrm e}^{5}+3 \,{\mathrm e}\right ) {\mathrm e}^{-1}}{16}\) | \(22\) |
norman | \(\frac {11 x^{2}}{4}+\frac {11 \left (8 \,{\mathrm e}^{5}+3 \,{\mathrm e}\right ) {\mathrm e}^{-1} x}{16}\) | \(23\) |
default | \(\frac {{\mathrm e}^{-1} \left (44 x^{2} {\mathrm e}+88 x \,{\mathrm e}^{5}+33 x \,{\mathrm e}\right )}{16}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 22, normalized size = 1.47 \begin {gather*} \frac {11}{16} \, {\left (8 \, x e^{5} + {\left (4 \, x^{2} + 3 \, x\right )} e\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 14, normalized size = 0.93 \begin {gather*} \frac {11}{4} \, x^{2} + \frac {11}{2} \, x e^{4} + \frac {33}{16} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 17, normalized size = 1.13 \begin {gather*} \frac {11 x^{2}}{4} + x \left (\frac {33}{16} + \frac {11 e^{4}}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 22, normalized size = 1.47 \begin {gather*} \frac {11}{16} \, {\left (8 \, x e^{5} + {\left (4 \, x^{2} + 3 \, x\right )} e\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.43, size = 13, normalized size = 0.87 \begin {gather*} \frac {11\,{\left (8\,x+8\,{\mathrm {e}}^4+3\right )}^2}{256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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