Optimal. Leaf size=13 \[ x+\left (-16 e^x+6 x\right )^2 \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(27\) vs. \(2(13)=26\).
time = 0.01, antiderivative size = 27, normalized size of antiderivative = 2.08, number of steps
used = 4, number of rules used = 2, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {2225, 2207}
\begin {gather*} 36 x^2+x+192 e^x+256 e^{2 x}-192 e^x (x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 2207
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+36 x^2+512 \int e^{2 x} \, dx+\int e^x (-192-192 x) \, dx\\ &=256 e^{2 x}+x+36 x^2-192 e^x (1+x)+192 \int e^x \, dx\\ &=192 e^x+256 e^{2 x}+x+36 x^2-192 e^x (1+x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 20, normalized size = 1.54 \begin {gather*} 256 e^{2 x}+x-192 e^x x+36 x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 19, normalized size = 1.46
method | result | size |
default | \(x -192 \,{\mathrm e}^{x} x +36 x^{2}+256 \,{\mathrm e}^{2 x}\) | \(19\) |
norman | \(x -192 \,{\mathrm e}^{x} x +36 x^{2}+256 \,{\mathrm e}^{2 x}\) | \(19\) |
risch | \(x -192 \,{\mathrm e}^{x} x +36 x^{2}+256 \,{\mathrm e}^{2 x}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 18, normalized size = 1.38 \begin {gather*} 36 \, x^{2} - 192 \, x e^{x} + x + 256 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 18, normalized size = 1.38 \begin {gather*} 36 \, x^{2} - 192 \, x e^{x} + x + 256 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 19, normalized size = 1.46 \begin {gather*} 36 x^{2} - 192 x e^{x} + x + 256 e^{2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 18, normalized size = 1.38 \begin {gather*} 36 \, x^{2} - 192 \, x e^{x} + x + 256 \, e^{\left (2 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.10, size = 18, normalized size = 1.38 \begin {gather*} x+256\,{\mathrm {e}}^{2\,x}-192\,x\,{\mathrm {e}}^x+36\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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