Optimal. Leaf size=16 \[ e^{4096 e^{8 x^2} x^2} x \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(54\) vs. \(2(16)=32\).
time = 0.02, antiderivative size = 54, normalized size of antiderivative = 3.38, number of steps
used = 1, number of rules used = 1, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {2326}
\begin {gather*} \frac {e^{4096 e^{8 x^2} x^2+8 x^2} \left (8 x^4+x^2\right )}{e^{8 x^2} x+8 e^{8 x^2} x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{8 x^2+4096 e^{8 x^2} x^2} \left (x^2+8 x^4\right )}{e^{8 x^2} x+8 e^{8 x^2} x^3}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 16, normalized size = 1.00 \begin {gather*} e^{4096 e^{8 x^2} x^2} x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 15, normalized size = 0.94
method | result | size |
risch | \({\mathrm e}^{4096 x^{2} {\mathrm e}^{8 x^{2}}} x\) | \(15\) |
norman | \({\mathrm e}^{4096 x^{2} {\mathrm e}^{8 x^{2}}} x\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 14, normalized size = 0.88 \begin {gather*} x e^{\left (4096 \, x^{2} e^{\left (8 \, x^{2}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 14, normalized size = 0.88 \begin {gather*} x e^{\left (4096 \, x^{2} e^{\left (8 \, x^{2}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.99, size = 14, normalized size = 0.88 \begin {gather*} x e^{4096 x^{2} e^{8 x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.52, size = 14, normalized size = 0.88 \begin {gather*} x\,{\mathrm {e}}^{4096\,x^2\,{\mathrm {e}}^{8\,x^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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