Optimal. Leaf size=31 \[ x+4 \left (x (2+x)+e^{e^4} \left (-2 x+e^5 \left (4+x^2\right )\right )\right )^2 \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(149\) vs. \(2(31)=62\).
time = 0.06, antiderivative size = 149, normalized size of antiderivative = 4.81, number of steps
used = 6, number of rules used = 0, integrand size = 85, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} 4 e^{2 \left (5+e^4\right )} x^4+8 e^{5+e^4} x^4+4 x^4-16 e^{5+2 e^4} x^3+16 e^{5+e^4} x^3-16 e^{e^4} x^3+16 x^3+32 e^{2 \left (5+e^4\right )} x^2+32 e^{5+e^4} x^2+16 e^{2 e^4} x^2-32 e^{e^4} x^2+16 x^2-64 e^{5+2 e^4} x+64 e^{5+e^4} x+x \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+16 x^2+16 x^3+4 x^4+e^{e^4} \int \left (-64 x-48 x^2+e^5 \left (64+64 x+48 x^2+32 x^3\right )\right ) \, dx+e^{2 e^4} \int \left (32 x+e^5 \left (-64-48 x^2\right )+e^{10} \left (64 x+16 x^3\right )\right ) \, dx\\ &=x+16 x^2-32 e^{e^4} x^2+16 e^{2 e^4} x^2+16 x^3-16 e^{e^4} x^3+4 x^4+e^{5+e^4} \int \left (64+64 x+48 x^2+32 x^3\right ) \, dx+e^{2 \left (5+e^4\right )} \int \left (64 x+16 x^3\right ) \, dx+e^{5+2 e^4} \int \left (-64-48 x^2\right ) \, dx\\ &=x+64 e^{5+e^4} x-64 e^{5+2 e^4} x+16 x^2-32 e^{e^4} x^2+16 e^{2 e^4} x^2+32 e^{5+e^4} x^2+32 e^{2 \left (5+e^4\right )} x^2+16 x^3-16 e^{e^4} x^3+16 e^{5+e^4} x^3-16 e^{5+2 e^4} x^3+4 x^4+8 e^{5+e^4} x^4+4 e^{2 \left (5+e^4\right )} x^4\\ \end {aligned} \end {gather*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(93\) vs. \(2(31)=62\).
time = 0.04, size = 93, normalized size = 3.00 \begin {gather*} x \left (1+16 x+16 e^{2 e^4} x+16 x^2+4 x^3-16 e^{e^4} x (2+x)-16 e^{5+2 e^4} \left (4+x^2\right )+4 e^{2 \left (5+e^4\right )} x \left (8+x^2\right )+8 e^{5+e^4} \left (8+4 x+2 x^2+x^3\right )\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. \(131\) vs.
\(2(50)=100\).
time = 0.48, size = 132, normalized size = 4.26
method | result | size |
norman | \(\left (4 \,{\mathrm e}^{10} {\mathrm e}^{2 \,{\mathrm e}^{4}}+8 \,{\mathrm e}^{5} {\mathrm e}^{{\mathrm e}^{4}}+4\right ) x^{4}+\left (-16 \,{\mathrm e}^{5} {\mathrm e}^{2 \,{\mathrm e}^{4}}+16 \,{\mathrm e}^{5} {\mathrm e}^{{\mathrm e}^{4}}-16 \,{\mathrm e}^{{\mathrm e}^{4}}+16\right ) x^{3}+\left (32 \,{\mathrm e}^{10} {\mathrm e}^{2 \,{\mathrm e}^{4}}+32 \,{\mathrm e}^{5} {\mathrm e}^{{\mathrm e}^{4}}+16 \,{\mathrm e}^{2 \,{\mathrm e}^{4}}-32 \,{\mathrm e}^{{\mathrm e}^{4}}+16\right ) x^{2}+\left (-64 \,{\mathrm e}^{5} {\mathrm e}^{2 \,{\mathrm e}^{4}}+64 \,{\mathrm e}^{5} {\mathrm e}^{{\mathrm e}^{4}}+1\right ) x\) | \(109\) |
gosper | \(x \left (4 \,{\mathrm e}^{10} {\mathrm e}^{2 \,{\mathrm e}^{4}} x^{3}+32 \,{\mathrm e}^{10} {\mathrm e}^{2 \,{\mathrm e}^{4}} x -16 \,{\mathrm e}^{5} {\mathrm e}^{2 \,{\mathrm e}^{4}} x^{2}+8 x^{3} {\mathrm e}^{5} {\mathrm e}^{{\mathrm e}^{4}}+16 x^{2} {\mathrm e}^{5} {\mathrm e}^{{\mathrm e}^{4}}-64 \,{\mathrm e}^{5} {\mathrm e}^{2 \,{\mathrm e}^{4}}+32 x \,{\mathrm e}^{5} {\mathrm e}^{{\mathrm e}^{4}}+16 \,{\mathrm e}^{2 \,{\mathrm e}^{4}} x -16 x^{2} {\mathrm e}^{{\mathrm e}^{4}}+4 x^{3}+64 \,{\mathrm e}^{5} {\mathrm e}^{{\mathrm e}^{4}}-32 x \,{\mathrm e}^{{\mathrm e}^{4}}+16 x^{2}+16 x +1\right )\) | \(122\) |
default | \(4 \,{\mathrm e}^{10} {\mathrm e}^{2 \,{\mathrm e}^{4}} x^{4}+32 \,{\mathrm e}^{10} {\mathrm e}^{2 \,{\mathrm e}^{4}} x^{2}-16 \,{\mathrm e}^{5} {\mathrm e}^{2 \,{\mathrm e}^{4}} x^{3}+8 x^{4} {\mathrm e}^{5} {\mathrm e}^{{\mathrm e}^{4}}+16 x^{3} {\mathrm e}^{5} {\mathrm e}^{{\mathrm e}^{4}}-64 \,{\mathrm e}^{5} {\mathrm e}^{2 \,{\mathrm e}^{4}} x +32 x^{2} {\mathrm e}^{5} {\mathrm e}^{{\mathrm e}^{4}}+16 \,{\mathrm e}^{2 \,{\mathrm e}^{4}} x^{2}-16 x^{3} {\mathrm e}^{{\mathrm e}^{4}}+4 x^{4}+64 x \,{\mathrm e}^{5} {\mathrm e}^{{\mathrm e}^{4}}-32 x^{2} {\mathrm e}^{{\mathrm e}^{4}}+16 x^{3}+16 x^{2}+x\) | \(132\) |
risch | \(4 \,{\mathrm e}^{10} {\mathrm e}^{2 \,{\mathrm e}^{4}} x^{4}+32 \,{\mathrm e}^{10} {\mathrm e}^{2 \,{\mathrm e}^{4}} x^{2}-16 \,{\mathrm e}^{5} {\mathrm e}^{2 \,{\mathrm e}^{4}} x^{3}+64 \,{\mathrm e}^{10} {\mathrm e}^{2 \,{\mathrm e}^{4}}-64 \,{\mathrm e}^{5} {\mathrm e}^{2 \,{\mathrm e}^{4}} x +16 \,{\mathrm e}^{2 \,{\mathrm e}^{4}} x^{2}+8 x^{4} {\mathrm e}^{5+{\mathrm e}^{4}}+16 x^{3} {\mathrm e}^{5+{\mathrm e}^{4}}+32 x^{2} {\mathrm e}^{5+{\mathrm e}^{4}}+64 x \,{\mathrm e}^{5+{\mathrm e}^{4}}-16 x^{3} {\mathrm e}^{{\mathrm e}^{4}}-32 x^{2} {\mathrm e}^{{\mathrm e}^{4}}+4 x^{4}+16 x^{3}+16 x^{2}+x\) | \(143\) |
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. 90 vs.
\(2 (28) = 56\).
time = 0.26, size = 90, normalized size = 2.90 \begin {gather*} 4 \, x^{4} + 16 \, x^{3} + 16 \, x^{2} + 4 \, {\left (4 \, x^{2} + {\left (x^{4} + 8 \, x^{2}\right )} e^{10} - 4 \, {\left (x^{3} + 4 \, x\right )} e^{5}\right )} e^{\left (2 \, e^{4}\right )} - 8 \, {\left (2 \, x^{3} + 4 \, x^{2} - {\left (x^{4} + 2 \, x^{3} + 4 \, x^{2} + 8 \, x\right )} e^{5}\right )} e^{\left (e^{4}\right )} + 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. 90 vs.
\(2 (28) = 56\).
time = 0.36, size = 90, normalized size = 2.90 \begin {gather*} 4 \, x^{4} + 16 \, x^{3} + 16 \, x^{2} + 4 \, {\left (4 \, x^{2} + {\left (x^{4} + 8 \, x^{2}\right )} e^{10} - 4 \, {\left (x^{3} + 4 \, x\right )} e^{5}\right )} e^{\left (2 \, e^{4}\right )} - 8 \, {\left (2 \, x^{3} + 4 \, x^{2} - {\left (x^{4} + 2 \, x^{3} + 4 \, x^{2} + 8 \, x\right )} e^{5}\right )} e^{\left (e^{4}\right )} + 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. 128 vs.
\(2 (51) = 102\).
time = 0.02, size = 128, normalized size = 4.13 \begin {gather*} x^{4} \cdot \left (4 + 8 e^{5} e^{e^{4}} + 4 e^{10} e^{2 e^{4}}\right ) + x^{3} \left (- 16 e^{5} e^{2 e^{4}} - 16 e^{e^{4}} + 16 + 16 e^{5} e^{e^{4}}\right ) + x^{2} \left (- 32 e^{e^{4}} + 16 + 32 e^{5} e^{e^{4}} + 16 e^{2 e^{4}} + 32 e^{10} e^{2 e^{4}}\right ) + x \left (- 64 e^{5} e^{2 e^{4}} + 1 + 64 e^{5} e^{e^{4}}\right ) \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. 90 vs.
\(2 (28) = 56\).
time = 0.41, size = 90, normalized size = 2.90 \begin {gather*} 4 \, x^{4} + 16 \, x^{3} + 16 \, x^{2} + 4 \, {\left (4 \, x^{2} + {\left (x^{4} + 8 \, x^{2}\right )} e^{10} - 4 \, {\left (x^{3} + 4 \, x\right )} e^{5}\right )} e^{\left (2 \, e^{4}\right )} - 8 \, {\left (2 \, x^{3} + 4 \, x^{2} - {\left (x^{4} + 2 \, x^{3} + 4 \, x^{2} + 8 \, x\right )} e^{5}\right )} e^{\left (e^{4}\right )} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.97, size = 99, normalized size = 3.19 \begin {gather*} \left (8\,{\mathrm {e}}^{{\mathrm {e}}^4+5}+4\,{\mathrm {e}}^{2\,{\mathrm {e}}^4+10}+4\right )\,x^4+\left (\frac {{\mathrm {e}}^{{\mathrm {e}}^4}\,\left (48\,{\mathrm {e}}^5-48\right )}{3}-16\,{\mathrm {e}}^{2\,{\mathrm {e}}^4+5}+16\right )\,x^3+\left (\frac {{\mathrm {e}}^{{\mathrm {e}}^4}\,\left (64\,{\mathrm {e}}^5-64\right )}{2}+\frac {{\mathrm {e}}^{2\,{\mathrm {e}}^4}\,\left (64\,{\mathrm {e}}^{10}+32\right )}{2}+16\right )\,x^2+\left (64\,{\mathrm {e}}^{{\mathrm {e}}^4+5}-64\,{\mathrm {e}}^{2\,{\mathrm {e}}^4+5}+1\right )\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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