Optimal. Leaf size=20 \[ \left (-3+e^4+x+x \left (e^x+\frac {16}{x}+x\right )\right )^2 \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(79\) vs. \(2(20)=40\).
time = 0.17, antiderivative size = 79, normalized size of antiderivative = 3.95, number of steps
used = 23, number of rules used = 4, integrand size = 67, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.060, Rules used = {1607, 2227,
2207, 2225} \begin {gather*} x^4+2 e^x x^3+2 x^3+2 e^x x^2+e^{2 x} x^2+27 x^2+26 e^x x+26 x-2 e^{x+4}+\frac {1}{2} e^4 (2 x+1)^2+2 e^{x+4} (x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 1607
Rule 2207
Rule 2225
Rule 2227
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=26 x+27 x^2+2 x^3+x^4+\frac {1}{2} e^4 (1+2 x)^2+\int e^{2 x} \left (2 x+2 x^2\right ) \, dx+\int e^x \left (26+30 x+8 x^2+2 x^3+e^4 (2+2 x)\right ) \, dx\\ &=26 x+27 x^2+2 x^3+x^4+\frac {1}{2} e^4 (1+2 x)^2+\int e^{2 x} x (2+2 x) \, dx+\int \left (26 e^x+30 e^x x+8 e^x x^2+2 e^x x^3+2 e^{4+x} (1+x)\right ) \, dx\\ &=26 x+27 x^2+2 x^3+x^4+\frac {1}{2} e^4 (1+2 x)^2+2 \int e^x x^3 \, dx+2 \int e^{4+x} (1+x) \, dx+8 \int e^x x^2 \, dx+26 \int e^x \, dx+30 \int e^x x \, dx+\int \left (2 e^{2 x} x+2 e^{2 x} x^2\right ) \, dx\\ &=26 e^x+26 x+30 e^x x+27 x^2+8 e^x x^2+2 x^3+2 e^x x^3+x^4+2 e^{4+x} (1+x)+\frac {1}{2} e^4 (1+2 x)^2-2 \int e^{4+x} \, dx+2 \int e^{2 x} x \, dx+2 \int e^{2 x} x^2 \, dx-6 \int e^x x^2 \, dx-16 \int e^x x \, dx-30 \int e^x \, dx\\ &=-4 e^x-2 e^{4+x}+26 x+14 e^x x+e^{2 x} x+27 x^2+2 e^x x^2+e^{2 x} x^2+2 x^3+2 e^x x^3+x^4+2 e^{4+x} (1+x)+\frac {1}{2} e^4 (1+2 x)^2-2 \int e^{2 x} x \, dx+12 \int e^x x \, dx+16 \int e^x \, dx-\int e^{2 x} \, dx\\ &=12 e^x-\frac {e^{2 x}}{2}-2 e^{4+x}+26 x+26 e^x x+27 x^2+2 e^x x^2+e^{2 x} x^2+2 x^3+2 e^x x^3+x^4+2 e^{4+x} (1+x)+\frac {1}{2} e^4 (1+2 x)^2-12 \int e^x \, dx+\int e^{2 x} \, dx\\ &=-2 e^{4+x}+26 x+26 e^x x+27 x^2+2 e^x x^2+e^{2 x} x^2+2 x^3+2 e^x x^3+x^4+2 e^{4+x} (1+x)+\frac {1}{2} e^4 (1+2 x)^2\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(59\) vs. \(2(20)=40\).
time = 0.15, size = 59, normalized size = 2.95 \begin {gather*} 26 x+2 e^4 x+27 x^2+2 e^4 x^2+e^{2 x} x^2+2 x^3+x^4+2 e^x \left (\left (13+e^4\right ) x+x^2+x^3\right ) \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. \(75\) vs.
\(2(18)=36\).
time = 0.63, size = 76, normalized size = 3.80
method | result | size |
norman | \(x^{4}+\left (2 \,{\mathrm e}^{4}+26\right ) x +\left (2 \,{\mathrm e}^{4}+27\right ) x^{2}+{\mathrm e}^{2 x} x^{2}+\left (2 \,{\mathrm e}^{4}+26\right ) x \,{\mathrm e}^{x}+2 x^{3}+2 \,{\mathrm e}^{x} x^{2}+2 \,{\mathrm e}^{x} x^{3}\) | \(60\) |
risch | \({\mathrm e}^{2 x} x^{2}+\left (2 x^{3}+2 x \,{\mathrm e}^{4}+2 x^{2}+26 x \right ) {\mathrm e}^{x}+2 x^{2} {\mathrm e}^{4}+2 x \,{\mathrm e}^{4}+x^{4}+2 x^{3}+27 x^{2}+26 x\) | \(60\) |
default | \(26 x +\left (2 x^{2}+2 x \right ) {\mathrm e}^{4}+26 \,{\mathrm e}^{x} x +2 \,{\mathrm e}^{x} x^{2}+2 \,{\mathrm e}^{x} x^{3}+2 \,{\mathrm e}^{4} {\mathrm e}^{x}+2 \,{\mathrm e}^{4} \left ({\mathrm e}^{x} x -{\mathrm e}^{x}\right )+{\mathrm e}^{2 x} x^{2}+27 x^{2}+2 x^{3}+x^{4}\) | \(76\) |
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. 51 vs.
\(2 (18) = 36\).
time = 0.26, size = 51, normalized size = 2.55 \begin {gather*} x^{4} + 2 \, x^{3} + x^{2} e^{\left (2 \, x\right )} + 27 \, x^{2} + 2 \, {\left (x^{2} + x\right )} e^{4} + 2 \, {\left (x^{3} + x^{2} + x {\left (e^{4} + 13\right )}\right )} e^{x} + 26 \, x \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. 52 vs.
\(2 (18) = 36\).
time = 0.36, size = 52, normalized size = 2.60 \begin {gather*} x^{4} + 2 \, x^{3} + x^{2} e^{\left (2 \, x\right )} + 27 \, x^{2} + 2 \, {\left (x^{2} + x\right )} e^{4} + 2 \, {\left (x^{3} + x^{2} + x e^{4} + 13 \, x\right )} e^{x} + 26 \, x \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. 58 vs.
\(2 (17) = 34\).
time = 0.13, size = 58, normalized size = 2.90 \begin {gather*} x^{4} + 2 x^{3} + x^{2} e^{2 x} + x^{2} \cdot \left (27 + 2 e^{4}\right ) + x \left (26 + 2 e^{4}\right ) + \left (2 x^{3} + 2 x^{2} + 26 x + 2 x e^{4}\right ) e^{x} \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. 55 vs.
\(2 (18) = 36\).
time = 0.44, size = 55, normalized size = 2.75 \begin {gather*} x^{4} + 2 \, x^{3} + x^{2} e^{\left (2 \, x\right )} + 27 \, x^{2} + 2 \, {\left (x^{2} + x\right )} e^{4} + 2 \, x e^{\left (x + 4\right )} + 2 \, {\left (x^{3} + x^{2} + 13 \, x\right )} e^{x} + 26 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 7.45, size = 21, normalized size = 1.05 \begin {gather*} x\,\left (x+{\mathrm {e}}^x+1\right )\,\left (x+2\,{\mathrm {e}}^4+x\,{\mathrm {e}}^x+x^2+26\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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