Optimal. Leaf size=29 \[ x-x^2 \left (5-x^4\right )^2+\left (-e^{18}+(2+x)^2\right )^2 \]
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Rubi [A] time = 0.01, antiderivative size = 37, normalized size of antiderivative = 1.28, number of steps used = 1, number of rules used = 0, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -x^{10}+10 x^6+x^4+8 x^3-x^2+33 x-2 e^{18} (x+2)^2 \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=33 x-x^2+8 x^3+x^4+10 x^6-x^{10}-2 e^{18} (2+x)^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 41, normalized size = 1.41 \begin {gather*} 33 x-8 e^{18} x-x^2-2 e^{18} x^2+8 x^3+x^4+10 x^6-x^{10} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.90, size = 38, normalized size = 1.31 \begin {gather*} -x^{10} + 10 \, x^{6} + x^{4} + 8 \, x^{3} - x^{2} - 2 \, {\left (x^{2} + 4 \, x\right )} e^{18} + 33 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 38, normalized size = 1.31 \begin {gather*} -x^{10} + 10 \, x^{6} + x^{4} + 8 \, x^{3} - x^{2} - 2 \, {\left (x^{2} + 4 \, x\right )} e^{18} + 33 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 38, normalized size = 1.31
method | result | size |
gosper | \(-x \left (x^{9}-10 x^{5}+2 \,{\mathrm e}^{18} x -x^{3}+8 \,{\mathrm e}^{18}-8 x^{2}+x -33\right )\) | \(38\) |
risch | \(-2 x^{2} {\mathrm e}^{18}-8 \,{\mathrm e}^{18} x -x^{10}+10 x^{6}+x^{4}+8 x^{3}-x^{2}+33 x\) | \(40\) |
default | \({\mathrm e}^{18} \left (-2 x^{2}-8 x \right )-x^{10}+10 x^{6}+x^{4}+8 x^{3}-x^{2}+33 x\) | \(42\) |
norman | \(x^{4}+\left (-8 \,{\mathrm e}^{18}+33\right ) x +\left (-2 \,{\mathrm e}^{18}-1\right ) x^{2}+8 x^{3}+10 x^{6}-x^{10}\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 38, normalized size = 1.31 \begin {gather*} -x^{10} + 10 \, x^{6} + x^{4} + 8 \, x^{3} - x^{2} - 2 \, {\left (x^{2} + 4 \, x\right )} e^{18} + 33 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.42, size = 39, normalized size = 1.34 \begin {gather*} -x^{10}+10\,x^6+x^4+8\,x^3+\left (-2\,{\mathrm {e}}^{18}-1\right )\,x^2+\left (33-8\,{\mathrm {e}}^{18}\right )\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 36, normalized size = 1.24 \begin {gather*} - x^{10} + 10 x^{6} + x^{4} + 8 x^{3} + x^{2} \left (- 2 e^{18} - 1\right ) + x \left (33 - 8 e^{18}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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