Optimal. Leaf size=25 \[ e^{3+x} x (2-x (2+2 x))^2 (-x+\log (x)) \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(109\) vs. \(2(25)=50\).
time = 0.85, antiderivative size = 109, normalized size of antiderivative = 4.36, number of steps
used = 50, number of rules used = 5, integrand size = 70, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2227, 2225,
2207, 2634, 12} \begin {gather*} -4 e^{x+3} x^6-8 e^{x+3} x^5+4 e^{x+3} x^5 \log (x)+4 e^{x+3} x^4+8 e^{x+3} x^4 \log (x)+8 e^{x+3} x^3-4 e^{x+3} x^3 \log (x)-4 e^{x+3} x^2-8 e^{x+3} x^2 \log (x)+4 e^{x+3} x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2207
Rule 2225
Rule 2227
Rule 2634
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{3+x} \left (4-16 x+16 x^2+32 x^3-32 x^4-32 x^5-4 x^6\right ) \, dx+\int e^{3+x} \left (4-12 x-20 x^2+28 x^3+28 x^4+4 x^5\right ) \log (x) \, dx\\ &=4 e^{3+x} x \log (x)-8 e^{3+x} x^2 \log (x)-4 e^{3+x} x^3 \log (x)+8 e^{3+x} x^4 \log (x)+4 e^{3+x} x^5 \log (x)-\int 4 e^{3+x} \left (1-x-x^2\right )^2 \, dx+\int \left (4 e^{3+x}-16 e^{3+x} x+16 e^{3+x} x^2+32 e^{3+x} x^3-32 e^{3+x} x^4-32 e^{3+x} x^5-4 e^{3+x} x^6\right ) \, dx\\ &=4 e^{3+x} x \log (x)-8 e^{3+x} x^2 \log (x)-4 e^{3+x} x^3 \log (x)+8 e^{3+x} x^4 \log (x)+4 e^{3+x} x^5 \log (x)+4 \int e^{3+x} \, dx-4 \int e^{3+x} x^6 \, dx-4 \int e^{3+x} \left (1-x-x^2\right )^2 \, dx-16 \int e^{3+x} x \, dx+16 \int e^{3+x} x^2 \, dx+32 \int e^{3+x} x^3 \, dx-32 \int e^{3+x} x^4 \, dx-32 \int e^{3+x} x^5 \, dx\\ &=4 e^{3+x}-16 e^{3+x} x+16 e^{3+x} x^2+32 e^{3+x} x^3-32 e^{3+x} x^4-32 e^{3+x} x^5-4 e^{3+x} x^6+4 e^{3+x} x \log (x)-8 e^{3+x} x^2 \log (x)-4 e^{3+x} x^3 \log (x)+8 e^{3+x} x^4 \log (x)+4 e^{3+x} x^5 \log (x)-4 \int \left (e^{3+x}-2 e^{3+x} x-e^{3+x} x^2+2 e^{3+x} x^3+e^{3+x} x^4\right ) \, dx+16 \int e^{3+x} \, dx+24 \int e^{3+x} x^5 \, dx-32 \int e^{3+x} x \, dx-96 \int e^{3+x} x^2 \, dx+128 \int e^{3+x} x^3 \, dx+160 \int e^{3+x} x^4 \, dx\\ &=20 e^{3+x}-48 e^{3+x} x-80 e^{3+x} x^2+160 e^{3+x} x^3+128 e^{3+x} x^4-8 e^{3+x} x^5-4 e^{3+x} x^6+4 e^{3+x} x \log (x)-8 e^{3+x} x^2 \log (x)-4 e^{3+x} x^3 \log (x)+8 e^{3+x} x^4 \log (x)+4 e^{3+x} x^5 \log (x)-4 \int e^{3+x} \, dx+4 \int e^{3+x} x^2 \, dx-4 \int e^{3+x} x^4 \, dx+8 \int e^{3+x} x \, dx-8 \int e^{3+x} x^3 \, dx+32 \int e^{3+x} \, dx-120 \int e^{3+x} x^4 \, dx+192 \int e^{3+x} x \, dx-384 \int e^{3+x} x^2 \, dx-640 \int e^{3+x} x^3 \, dx\\ &=48 e^{3+x}+152 e^{3+x} x-460 e^{3+x} x^2-488 e^{3+x} x^3+4 e^{3+x} x^4-8 e^{3+x} x^5-4 e^{3+x} x^6+4 e^{3+x} x \log (x)-8 e^{3+x} x^2 \log (x)-4 e^{3+x} x^3 \log (x)+8 e^{3+x} x^4 \log (x)+4 e^{3+x} x^5 \log (x)-8 \int e^{3+x} \, dx-8 \int e^{3+x} x \, dx+16 \int e^{3+x} x^3 \, dx+24 \int e^{3+x} x^2 \, dx-192 \int e^{3+x} \, dx+480 \int e^{3+x} x^3 \, dx+768 \int e^{3+x} x \, dx+1920 \int e^{3+x} x^2 \, dx\\ &=-152 e^{3+x}+912 e^{3+x} x+1484 e^{3+x} x^2+8 e^{3+x} x^3+4 e^{3+x} x^4-8 e^{3+x} x^5-4 e^{3+x} x^6+4 e^{3+x} x \log (x)-8 e^{3+x} x^2 \log (x)-4 e^{3+x} x^3 \log (x)+8 e^{3+x} x^4 \log (x)+4 e^{3+x} x^5 \log (x)+8 \int e^{3+x} \, dx-48 \int e^{3+x} x \, dx-48 \int e^{3+x} x^2 \, dx-768 \int e^{3+x} \, dx-1440 \int e^{3+x} x^2 \, dx-3840 \int e^{3+x} x \, dx\\ &=-912 e^{3+x}-2976 e^{3+x} x-4 e^{3+x} x^2+8 e^{3+x} x^3+4 e^{3+x} x^4-8 e^{3+x} x^5-4 e^{3+x} x^6+4 e^{3+x} x \log (x)-8 e^{3+x} x^2 \log (x)-4 e^{3+x} x^3 \log (x)+8 e^{3+x} x^4 \log (x)+4 e^{3+x} x^5 \log (x)+48 \int e^{3+x} \, dx+96 \int e^{3+x} x \, dx+2880 \int e^{3+x} x \, dx+3840 \int e^{3+x} \, dx\\ &=2976 e^{3+x}-4 e^{3+x} x^2+8 e^{3+x} x^3+4 e^{3+x} x^4-8 e^{3+x} x^5-4 e^{3+x} x^6+4 e^{3+x} x \log (x)-8 e^{3+x} x^2 \log (x)-4 e^{3+x} x^3 \log (x)+8 e^{3+x} x^4 \log (x)+4 e^{3+x} x^5 \log (x)-96 \int e^{3+x} \, dx-2880 \int e^{3+x} \, dx\\ &=-4 e^{3+x} x^2+8 e^{3+x} x^3+4 e^{3+x} x^4-8 e^{3+x} x^5-4 e^{3+x} x^6+4 e^{3+x} x \log (x)-8 e^{3+x} x^2 \log (x)-4 e^{3+x} x^3 \log (x)+8 e^{3+x} x^4 \log (x)+4 e^{3+x} x^5 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.12, size = 22, normalized size = 0.88 \begin {gather*} -4 e^{3+x} x \left (-1+x+x^2\right )^2 (x-\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(82\) vs.
\(2(26)=52\).
time = 0.32, size = 83, normalized size = 3.32
method | result | size |
risch | \(4 \ln \left (x \right ) x \left (x^{4}+2 x^{3}-x^{2}-2 x +1\right ) {\mathrm e}^{3+x}-4 \left (x^{4}-2 x^{3}+5 x^{2}-12 x +13\right ) {\mathrm e}^{3+x}+\left (-4 x^{6}-8 x^{5}+8 x^{4}+16 x^{2}-48 x +52\right ) {\mathrm e}^{3+x}\) | \(83\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 262 vs.
\(2 (22) = 44\).
time = 0.27, size = 262, normalized size = 10.48 \begin {gather*} 4 \, {\left (x^{5} e^{3} + 2 \, x^{4} e^{3} - x^{3} e^{3} - 2 \, x^{2} e^{3} + x e^{3}\right )} e^{x} \log \left (x\right ) - 4 \, {\left (x^{6} e^{3} - 6 \, x^{5} e^{3} + 30 \, x^{4} e^{3} - 120 \, x^{3} e^{3} + 360 \, x^{2} e^{3} - 720 \, x e^{3} + 720 \, e^{3}\right )} e^{x} - 32 \, {\left (x^{5} e^{3} - 5 \, x^{4} e^{3} + 20 \, x^{3} e^{3} - 60 \, x^{2} e^{3} + 120 \, x e^{3} - 120 \, e^{3}\right )} e^{x} - 4 \, {\left (x^{4} e^{3} - 2 \, x^{3} e^{3} + 5 \, x^{2} e^{3} - 12 \, x e^{3} + 13 \, e^{3}\right )} e^{x} - 32 \, {\left (x^{4} e^{3} - 4 \, x^{3} e^{3} + 12 \, x^{2} e^{3} - 24 \, x e^{3} + 24 \, e^{3}\right )} e^{x} + 32 \, {\left (x^{3} e^{3} - 3 \, x^{2} e^{3} + 6 \, x e^{3} - 6 \, e^{3}\right )} e^{x} + 16 \, {\left (x^{2} e^{3} - 2 \, x e^{3} + 2 \, e^{3}\right )} e^{x} - 16 \, {\left (x e^{3} - e^{3}\right )} e^{x} + 4 \, e^{\left (x + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 57 vs.
\(2 (22) = 44\).
time = 0.35, size = 57, normalized size = 2.28 \begin {gather*} 4 \, {\left (x^{5} + 2 \, x^{4} - x^{3} - 2 \, x^{2} + x\right )} e^{\left (x + 3\right )} \log \left (x\right ) - 4 \, {\left (x^{6} + 2 \, x^{5} - x^{4} - 2 \, x^{3} + x^{2}\right )} e^{\left (x + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 104 vs.
\(2 (24) = 48\).
time = 0.17, size = 104, normalized size = 4.16 \begin {gather*} \left (- 4 x^{6} e^{2} + 4 x^{5} e^{2} \log {\left (x \right )} - 8 x^{5} e^{2} + 8 x^{4} e^{2} \log {\left (x \right )} + 4 x^{4} e^{2} - 4 x^{3} e^{2} \log {\left (x \right )} + 8 x^{3} e^{2} - 8 x^{2} e^{2} \log {\left (x \right )} - 4 x^{2} e^{2} + 4 x e^{2} \log {\left (x \right )}\right ) e^{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. 130 vs.
\(2 (22) = 44\).
time = 0.42, size = 130, normalized size = 5.20 \begin {gather*} 4 \, {\left (x^{5} + 2 \, x^{4} - x^{3} - 2 \, x^{2} + x\right )} e^{\left (x + 3\right )} \log \left (x\right ) - 4 \, {\left (x^{6} + 2 \, x^{5} - 2 \, x^{4} - 4 \, x^{2} + 12 \, x - 13\right )} e^{\left (x + 3\right )} - 4 \, {\left (x^{4} - 4 \, x^{3} + 12 \, x^{2} - 24 \, x + 24\right )} e^{\left (x + 3\right )} - 8 \, {\left (x^{3} - 3 \, x^{2} + 6 \, x - 6\right )} e^{\left (x + 3\right )} + 4 \, {\left (x^{2} - 2 \, x + 2\right )} e^{\left (x + 3\right )} + 8 \, {\left (x - 1\right )} e^{\left (x + 3\right )} - 4 \, e^{\left (x + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.59, size = 21, normalized size = 0.84 \begin {gather*} -4\,x\,{\mathrm {e}}^{x+3}\,\left (x-\ln \left (x\right )\right )\,{\left (x^2+x-1\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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