Optimal. Leaf size=20 \[ 5+\frac {5}{x}+14 e^{4 x \left (x+x^2\right )} x \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(41\) vs. \(2(20)=40\).
time = 0.05, antiderivative size = 41, normalized size of antiderivative = 2.05, number of steps
used = 3, number of rules used = 2, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {14, 2326}
\begin {gather*} \frac {14 e^{4 x^2 (x+1)} \left (3 x^3+2 x^2\right )}{x^2+2 (x+1) x}+\frac {5}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {5}{x^2}+14 e^{4 x^2 (1+x)} \left (1+8 x^2+12 x^3\right )\right ) \, dx\\ &=\frac {5}{x}+14 \int e^{4 x^2 (1+x)} \left (1+8 x^2+12 x^3\right ) \, dx\\ &=\frac {5}{x}+\frac {14 e^{4 x^2 (1+x)} \left (2 x^2+3 x^3\right )}{x^2+2 x (1+x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 19, normalized size = 0.95 \begin {gather*} \frac {5}{x}+14 e^{4 x^2 (1+x)} x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 19, normalized size = 0.95
method | result | size |
risch | \(\frac {5}{x}+14 x \,{\mathrm e}^{4 \left (x +1\right ) x^{2}}\) | \(19\) |
norman | \(\frac {5+14 \,{\mathrm e}^{4 x^{3}+4 x^{2}} x^{2}}{x}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 21, normalized size = 1.05 \begin {gather*} 14 \, x e^{\left (4 \, x^{3} + 4 \, x^{2}\right )} + \frac {5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 23, normalized size = 1.15 \begin {gather*} \frac {14 \, x^{2} e^{\left (4 \, x^{3} + 4 \, x^{2}\right )} + 5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 17, normalized size = 0.85 \begin {gather*} 14 x e^{4 x^{3} + 4 x^{2}} + \frac {5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 23, normalized size = 1.15 \begin {gather*} \frac {14 \, x^{2} e^{\left (4 \, x^{3} + 4 \, x^{2}\right )} + 5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.81, size = 21, normalized size = 1.05 \begin {gather*} 14\,x\,{\mathrm {e}}^{4\,x^3+4\,x^2}+\frac {5}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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