Optimal. Leaf size=22 \[ -5+x+4 \left (5-4 e (1-x) x^2\right )^2+\log (2) \]
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Rubi [A]
time = 0.02, antiderivative size = 38, normalized size of antiderivative = 1.73, number of steps
used = 2, number of rules used = 1, integrand size = 55, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {1600}
\begin {gather*} 64 e^2 x^6-128 e^2 x^5+64 e^2 x^4+160 e x^3-160 e x^2+x \end {gather*}
Antiderivative was successfully verified.
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Rule 1600
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-320 e x+480 e x^2+256 e^2 x^3-640 e^2 x^4+384 e^2 x^5\right ) \, dx\\ &=x-160 e x^2+160 e x^3+64 e^2 x^4-128 e^2 x^5+64 e^2 x^6\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 38, normalized size = 1.73 \begin {gather*} x-160 e x^2+160 e x^3+64 e^2 x^4-128 e^2 x^5+64 e^2 x^6 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.91, size = 36, normalized size = 1.64
method | result | size |
default | \(x +128 \,{\mathrm e}^{2} \left (\frac {1}{2} x^{6}-x^{5}+\frac {1}{2} x^{4}\right )-160 \,{\mathrm e} \left (-x^{3}+x^{2}\right )\) | \(36\) |
risch | \(x -160 x^{2} {\mathrm e}+160 x^{3} {\mathrm e}+64 x^{4} {\mathrm e}^{2}-128 \,{\mathrm e}^{2} x^{5}+64 x^{6} {\mathrm e}^{2}\) | \(38\) |
norman | \(x -160 x^{2} {\mathrm e}+160 x^{3} {\mathrm e}+64 x^{4} {\mathrm e}^{2}-128 \,{\mathrm e}^{2} x^{5}+64 x^{6} {\mathrm e}^{2}\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 37, normalized size = 1.68 \begin {gather*} 64 \, x^{6} e^{2} - 128 \, x^{5} e^{2} + 64 \, x^{4} e^{2} + 160 \, x^{3} e - 160 \, x^{2} e + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 41, normalized size = 1.86 \begin {gather*} 4 \, {\left (x^{6} - 2 \, x^{5} + x^{4}\right )} e^{\left (4 \, \log \left (2\right ) + 2\right )} + 40 \, {\left (x^{3} - x^{2}\right )} e^{\left (2 \, \log \left (2\right ) + 1\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. 42 vs.
\(2 (20) = 40\).
time = 0.02, size = 42, normalized size = 1.91 \begin {gather*} 64 x^{6} e^{2} - 128 x^{5} e^{2} + 64 x^{4} e^{2} + 160 e x^{3} - 160 e x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.45, size = 37, normalized size = 1.68 \begin {gather*} 64 \, x^{6} e^{2} - 128 \, x^{5} e^{2} + 64 \, x^{4} e^{2} + 160 \, x^{3} e - 160 \, x^{2} e + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.10, size = 37, normalized size = 1.68 \begin {gather*} 64\,{\mathrm {e}}^2\,x^6-128\,{\mathrm {e}}^2\,x^5+64\,{\mathrm {e}}^2\,x^4+160\,\mathrm {e}\,x^3-160\,\mathrm {e}\,x^2+x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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