Optimal. Leaf size=22 \[ \left (25+\frac {e^{-1+e^{2 x}}}{x}\right ) x^2 (e+x) \]
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Rubi [A]
time = 0.02, antiderivative size = 29, normalized size of antiderivative = 1.32, number of steps
used = 2, number of rules used = 1, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {2326}
\begin {gather*} 25 x^3+25 e x^2+e^{e^{2 x}-1} \left (x^2+e x\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=25 e x^2+25 x^3+\int e^{-1+e^{2 x}} \left (e+2 x+e^{2 x} \left (2 e x+2 x^2\right )\right ) \, dx\\ &=25 e x^2+25 x^3+e^{-1+e^{2 x}} \left (e x+x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 26, normalized size = 1.18 \begin {gather*} 25 e x^2+25 x^3+e^{-1+e^{2 x}} x (e+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 36, normalized size = 1.64
method | result | size |
risch | \(\left (x \,{\mathrm e}+x^{2}\right ) {\mathrm e}^{{\mathrm e}^{2 x}-1}+25 x^{2} {\mathrm e}+25 x^{3}\) | \(30\) |
default | \(x^{2} {\mathrm e}^{{\mathrm e}^{2 x}-1}+x \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{2 x}-1}+25 x^{3}+25 x^{2} {\mathrm e}\) | \(36\) |
norman | \(x^{2} {\mathrm e}^{{\mathrm e}^{2 x}-1}+x \,{\mathrm e} \,{\mathrm e}^{{\mathrm e}^{2 x}-1}+25 x^{3}+25 x^{2} {\mathrm e}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 29, normalized size = 1.32 \begin {gather*} 25 \, x^{3} + 25 \, x^{2} e + {\left (x^{2} + x e\right )} e^{\left (e^{\left (2 \, x\right )} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 29, normalized size = 1.32 \begin {gather*} 25 \, x^{3} + 25 \, x^{2} e + {\left (x^{2} + x e\right )} e^{\left (e^{\left (2 \, x\right )} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 29, normalized size = 1.32 \begin {gather*} 25 x^{3} + 25 e x^{2} + \left (x^{2} + e x\right ) e^{e^{2 x} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 46 vs.
\(2 (21) = 42\).
time = 0.41, size = 46, normalized size = 2.09 \begin {gather*} 25 \, x^{3} + 25 \, x^{2} e + {\left (x^{2} e^{\left (2 \, x + e^{\left (2 \, x\right )}\right )} + x e^{\left (2 \, x + e^{\left (2 \, x\right )} + 1\right )}\right )} e^{\left (-2 \, x - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.29, size = 19, normalized size = 0.86 \begin {gather*} x\,{\mathrm {e}}^{-1}\,\left (x+\mathrm {e}\right )\,\left ({\mathrm {e}}^{{\mathrm {e}}^{2\,x}}+25\,x\,\mathrm {e}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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