Optimal. Leaf size=19 \[ x^2+x \left (-1+e^8+e^{10}+x^2\right )^2 \]
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Rubi [B] time = 0.02, antiderivative size = 57, normalized size of antiderivative = 3.00, number of steps used = 3, number of rules used = 0, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^5+2 e^{10} x^3+2 e^8 x^3-2 x^3+x^2+\left (1+e^{16}+e^{20}\right ) x-2 e^{10} \left (1-e^8\right ) x-2 e^8 x \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\left (1+e^{16}+e^{20}\right ) x+x^2-2 x^3+x^5+e^8 \int \left (-2+6 x^2\right ) \, dx+e^{10} \int \left (-2+2 e^8+6 x^2\right ) \, dx\\ &=-2 e^8 x-2 e^{10} \left (1-e^8\right ) x+\left (1+e^{16}+e^{20}\right ) x+x^2-2 x^3+2 e^8 x^3+2 e^{10} x^3+x^5\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.01, size = 56, normalized size = 2.95 \begin {gather*} x-2 e^8 x+e^{16} x+e^{20} x+2 e^{10} \left (-1+e^8\right ) x+x^2-2 x^3+2 e^8 x^3+2 e^{10} x^3+x^5 \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.66, size = 48, normalized size = 2.53 \begin {gather*} x^{5} - 2 \, x^{3} + x^{2} + x e^{20} + 2 \, x e^{18} + x e^{16} + 2 \, {\left (x^{3} - x\right )} e^{10} + 2 \, {\left (x^{3} - x\right )} e^{8} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.25, size = 47, normalized size = 2.47 \begin {gather*} x^{5} - 2 \, x^{3} + x^{2} + x e^{20} + x e^{16} + 2 \, {\left (x^{3} + x e^{8} - x\right )} e^{10} + 2 \, {\left (x^{3} - x\right )} e^{8} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 51, normalized size = 2.68
method | result | size |
risch | \(x \,{\mathrm e}^{20}+2 \,{\mathrm e}^{18} x +2 x^{3} {\mathrm e}^{10}-2 x \,{\mathrm e}^{10}+x \,{\mathrm e}^{16}+2 \,{\mathrm e}^{8} x^{3}-2 x \,{\mathrm e}^{8}+x^{5}-2 x^{3}+x^{2}+x\) | \(51\) |
norman | \(x^{5}+\left (2 \,{\mathrm e}^{8}+2 \,{\mathrm e}^{10}-2\right ) x^{3}+x^{2}+\left ({\mathrm e}^{16}+2 \,{\mathrm e}^{10} {\mathrm e}^{8}+{\mathrm e}^{20}-2 \,{\mathrm e}^{8}-2 \,{\mathrm e}^{10}+1\right ) x\) | \(54\) |
gosper | \(x \left ({\mathrm e}^{16}+2 x^{2} {\mathrm e}^{8}+x^{4}+2 \,{\mathrm e}^{10} {\mathrm e}^{8}+2 \,{\mathrm e}^{10} x^{2}+{\mathrm e}^{20}-2 \,{\mathrm e}^{8}-2 x^{2}-2 \,{\mathrm e}^{10}+x +1\right )\) | \(56\) |
default | \(x \,{\mathrm e}^{20}+{\mathrm e}^{10} \left (2 x \,{\mathrm e}^{8}+2 x^{3}-2 x \right )+x \,{\mathrm e}^{16}+{\mathrm e}^{8} \left (2 x^{3}-2 x \right )+x^{5}-2 x^{3}+x^{2}+x\) | \(59\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.34, size = 47, normalized size = 2.47 \begin {gather*} x^{5} - 2 \, x^{3} + x^{2} + x e^{20} + x e^{16} + 2 \, {\left (x^{3} + x e^{8} - x\right )} e^{10} + 2 \, {\left (x^{3} - x\right )} e^{8} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.43, size = 42, normalized size = 2.21 \begin {gather*} x^5+\left (2\,{\mathrm {e}}^8+2\,{\mathrm {e}}^{10}-2\right )\,x^3+x^2+\left ({\mathrm {e}}^{16}-2\,{\mathrm {e}}^8+{\mathrm {e}}^{20}+{\mathrm {e}}^{10}\,\left (2\,{\mathrm {e}}^8-2\right )+1\right )\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.06, size = 46, normalized size = 2.42 \begin {gather*} x^{5} + x^{3} \left (-2 + 2 e^{8} + 2 e^{10}\right ) + x^{2} + x \left (- 2 e^{10} - 2 e^{8} + 1 + e^{16} + 2 e^{18} + e^{20}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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