Optimal. Leaf size=23 \[ 3+\frac {e^{3 \left (x+3 e^{4+x} x\right )} x}{2+x} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(65\) vs. \(2(23)=46\).
time = 0.31, antiderivative size = 65, normalized size of antiderivative = 2.83, number of steps
used = 2, number of rules used = 2, integrand size = 55, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {27, 2326}
\begin {gather*} \frac {e^{9 e^{x+4} x+3 x} \left (x^2+3 e^{x+4} \left (x^3+3 x^2+2 x\right )+2 x\right )}{(x+2)^2 \left (3 e^{x+4} x+3 e^{x+4}+1\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{3 x+9 e^{4+x} x} \left (2+6 x+3 x^2+e^{4+x} \left (18 x+27 x^2+9 x^3\right )\right )}{(2+x)^2} \, dx\\ &=\frac {e^{3 x+9 e^{4+x} x} \left (2 x+x^2+3 e^{4+x} \left (2 x+3 x^2+x^3\right )\right )}{(2+x)^2 \left (1+3 e^{4+x}+3 e^{4+x} x\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.15, size = 21, normalized size = 0.91 \begin {gather*} \frac {e^{3 x+9 e^{4+x} x} x}{2+x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.06, size = 20, normalized size = 0.87
method | result | size |
norman | \(\frac {{\mathrm e}^{9 x \,{\mathrm e}^{4} {\mathrm e}^{x}+3 x} x}{2+x}\) | \(20\) |
risch | \(\frac {{\mathrm e}^{3 x \left (3 \,{\mathrm e}^{4+x}+1\right )} x}{2+x}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 19, normalized size = 0.83 \begin {gather*} \frac {x e^{\left (9 \, x e^{\left (x + 4\right )} + 3 \, x\right )}}{x + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 19, normalized size = 0.83 \begin {gather*} \frac {x e^{\left (9 \, x e^{\left (x + 4\right )} + 3 \, x\right )}}{x + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 19, normalized size = 0.83 \begin {gather*} \frac {x e^{9 x e^{4} e^{x} + 3 x}}{x + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.06, size = 19, normalized size = 0.83 \begin {gather*} \frac {x\,{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{9\,x\,{\mathrm {e}}^4\,{\mathrm {e}}^x}}{x+2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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