Optimal. Leaf size=13 \[ x-2 e^2 x (2+x)+\log (7) \]
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Rubi [A]
time = 0.00, antiderivative size = 12, normalized size of antiderivative = 0.92, number of steps
used = 1, number of rules used = 0, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} x-2 e^2 (x+1)^2 \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x-2 e^2 (1+x)^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 1.23 \begin {gather*} x-4 e^2 x-2 e^2 x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 15, normalized size = 1.15
method | result | size |
gosper | \(-x \left (2 \,{\mathrm e}^{2} x +4 \,{\mathrm e}^{2}-1\right )\) | \(15\) |
default | \(-2 x^{2} {\mathrm e}^{2}-4 \,{\mathrm e}^{2} x +x\) | \(15\) |
risch | \(-2 x^{2} {\mathrm e}^{2}-4 \,{\mathrm e}^{2} x +x\) | \(15\) |
norman | \(\left (-4 \,{\mathrm e}^{2}+1\right ) x -2 x^{2} {\mathrm e}^{2}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 13, normalized size = 1.00 \begin {gather*} -2 \, {\left (x^{2} + 2 \, x\right )} e^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.32, size = 13, normalized size = 1.00 \begin {gather*} -2 \, {\left (x^{2} + 2 \, x\right )} e^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 15, normalized size = 1.15 \begin {gather*} - 2 x^{2} e^{2} + x \left (1 - 4 e^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 13, normalized size = 1.00 \begin {gather*} -2 \, {\left (x^{2} + 2 \, x\right )} e^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.14, size = 17, normalized size = 1.31 \begin {gather*} -\frac {\left (4\,x+4\right )\,\left ({\mathrm {e}}^2\,\left (4\,x+4\right )-2\right )}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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