Optimal. Leaf size=22 \[ -4071+4 \left (\frac {5}{2 e-x}-x\right )-x \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.68, number of steps used = 3, number of rules used = 2, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {27, 683} \begin {gather*} \frac {20}{2 e-x}-5 x \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 683
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {20-20 e^2+20 e x-5 x^2}{(-2 e+x)^2} \, dx\\ &=\int \left (-5+\frac {20}{(2 e-x)^2}\right ) \, dx\\ &=\frac {20}{2 e-x}-5 x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 13, normalized size = 0.59 \begin {gather*} -5 \left (x+\frac {4}{-2 e+x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 20, normalized size = 0.91 \begin {gather*} -\frac {5 \, {\left (x^{2} - 2 \, x e + 4\right )}}{x - 2 \, e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: NotImplementedError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 15, normalized size = 0.68
method | result | size |
risch | \(-5 x +\frac {10}{{\mathrm e}-\frac {x}{2}}\) | \(15\) |
norman | \(\frac {5 x^{2}+20-20 \,{\mathrm e}^{2}}{2 \,{\mathrm e}-x}\) | \(25\) |
gosper | \(-\frac {5 \left (-x^{2}-4+4 \,{\mathrm e}^{2}\right )}{2 \,{\mathrm e}-x}\) | \(26\) |
meijerg | \(-\frac {5 x}{1-\frac {{\mathrm e}^{-1} x}{2}}+\frac {5 \,{\mathrm e}^{-2} x}{1-\frac {{\mathrm e}^{-1} x}{2}}+20 \,{\mathrm e} \left (\frac {{\mathrm e}^{-1} x}{2-{\mathrm e}^{-1} x}+\ln \left (1-\frac {{\mathrm e}^{-1} x}{2}\right )\right )+10 \,{\mathrm e} \left (-\frac {x \,{\mathrm e}^{-1} \left (-\frac {3 \,{\mathrm e}^{-1} x}{2}+6\right )}{6 \left (1-\frac {{\mathrm e}^{-1} x}{2}\right )}-2 \ln \left (1-\frac {{\mathrm e}^{-1} x}{2}\right )\right )\) | \(91\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 14, normalized size = 0.64 \begin {gather*} -5 \, x - \frac {20}{x - 2 \, e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 14, normalized size = 0.64 \begin {gather*} -5\,x-\frac {20}{x-2\,\mathrm {e}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 12, normalized size = 0.55 \begin {gather*} - 5 x - \frac {20}{x - 2 e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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