Optimal. Leaf size=16 \[ x^2-x \left (\frac {4}{e^{26}}+x^2\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 15, normalized size of antiderivative = 0.94, number of steps used = 4, number of rules used = 2, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {6688, 43} \begin {gather*} -x^3+x^2-\frac {4 x}{e^{26}} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {4}{e^{26}}+(2-3 x) x\right ) \, dx\\ &=-\frac {4 x}{e^{26}}+\int (2-3 x) x \, dx\\ &=-\frac {4 x}{e^{26}}+\int \left (2 x-3 x^2\right ) \, dx\\ &=-\frac {4 x}{e^{26}}+x^2-x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 0.94 \begin {gather*} -\frac {4 x}{e^{26}}+x^2-x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 20, normalized size = 1.25 \begin {gather*} -{\left ({\left (x^{3} - x^{2}\right )} e^{26} + 4 \, x\right )} e^{\left (-26\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 21, normalized size = 1.31 \begin {gather*} -{\left (x^{3} e^{26} - x^{2} e^{26} + 4 \, x\right )} e^{\left (-26\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 15, normalized size = 0.94
method | result | size |
risch | \(-x^{3}+x^{2}-4 x \,{\mathrm e}^{-26}\) | \(15\) |
default | \(-x^{3}+x^{2}-4 x \,{\mathrm e}^{-26}\) | \(17\) |
norman | \(\left ({\mathrm e}^{x} x^{2}-{\mathrm e}^{x} x^{3}-4 \,{\mathrm e}^{-26} x \,{\mathrm e}^{x}\right ) {\mathrm e}^{-x}\) | \(29\) |
meijerg | \(-\frac {3 \,{\mathrm e}^{x \,{\mathrm e}^{-26}-x +78} \left (2-\frac {\left (3 x^{2} {\mathrm e}^{-52} \left (-{\mathrm e}^{26}+1\right )^{2}+6 x \,{\mathrm e}^{-26} \left (-{\mathrm e}^{26}+1\right )+6\right ) {\mathrm e}^{-x \,{\mathrm e}^{-26} \left (-{\mathrm e}^{26}+1\right )}}{3}\right )}{\left (-{\mathrm e}^{26}+1\right )^{3}}+\frac {2 \,{\mathrm e}^{x \,{\mathrm e}^{-26}-x +52} \left (1-\frac {\left (2+2 x \,{\mathrm e}^{-26} \left (-{\mathrm e}^{26}+1\right )\right ) {\mathrm e}^{-x \,{\mathrm e}^{-26} \left (-{\mathrm e}^{26}+1\right )}}{2}\right )}{\left (-{\mathrm e}^{26}+1\right )^{2}}-\frac {4 \,{\mathrm e}^{x \,{\mathrm e}^{-26}-x} \left (1-{\mathrm e}^{-x \,{\mathrm e}^{-26} \left (-{\mathrm e}^{26}+1\right )}\right )}{-{\mathrm e}^{26}+1}\) | \(150\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 14, normalized size = 0.88 \begin {gather*} -x^{3} + x^{2} - 4 \, x e^{\left (-26\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 14, normalized size = 0.88 \begin {gather*} -x\,\left (x^2-x+4\,{\mathrm {e}}^{-26}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 12, normalized size = 0.75 \begin {gather*} - x^{3} + x^{2} - \frac {4 x}{e^{26}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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