Optimal. Leaf size=25 \[ 25+\frac {4 \left (2+\left (-1+e^2\right )^2\right )^2}{(1-x)^2}-x \]
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Rubi [A] time = 0.05, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 51, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {2074} \begin {gather*} \frac {4 \left (3-2 e^2+e^4\right )^2}{(1-x)^2}-x \end {gather*}
Antiderivative was successfully verified.
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Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1-\frac {8 \left (3-2 e^2+e^4\right )^2}{(-1+x)^3}\right ) \, dx\\ &=\frac {4 \left (3-2 e^2+e^4\right )^2}{(1-x)^2}-x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 23, normalized size = 0.92 \begin {gather*} \frac {4 \left (3-2 e^2+e^4\right )^2}{(-1+x)^2}-x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 39, normalized size = 1.56 \begin {gather*} -\frac {x^{3} - 2 \, x^{2} + x - 4 \, e^{8} + 16 \, e^{6} - 40 \, e^{4} + 48 \, e^{2} - 36}{x^{2} - 2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 27, normalized size = 1.08 \begin {gather*} -x + \frac {4 \, {\left (e^{8} - 4 \, e^{6} + 10 \, e^{4} - 12 \, e^{2} + 9\right )}}{{\left (x - 1\right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 30, normalized size = 1.20
method | result | size |
default | \(-x -\frac {-72+96 \,{\mathrm e}^{2}-80 \,{\mathrm e}^{4}-8 \,{\mathrm e}^{8}+32 \,{\mathrm e}^{6}}{2 \left (x -1\right )^{2}}\) | \(30\) |
gosper | \(\frac {4 \,{\mathrm e}^{8}-16 \,{\mathrm e}^{6}-x^{3}+40 \,{\mathrm e}^{4}-48 \,{\mathrm e}^{2}+3 x +34}{x^{2}-2 x +1}\) | \(44\) |
risch | \(-x +\frac {4 \,{\mathrm e}^{8}}{x^{2}-2 x +1}-\frac {16 \,{\mathrm e}^{6}}{x^{2}-2 x +1}+\frac {40 \,{\mathrm e}^{4}}{x^{2}-2 x +1}-\frac {48 \,{\mathrm e}^{2}}{x^{2}-2 x +1}+\frac {36}{x^{2}-2 x +1}\) | \(73\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 32, normalized size = 1.28 \begin {gather*} -x + \frac {4 \, {\left (e^{8} - 4 \, e^{6} + 10 \, e^{4} - 12 \, e^{2} + 9\right )}}{x^{2} - 2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 28, normalized size = 1.12 \begin {gather*} \frac {40\,{\mathrm {e}}^4-48\,{\mathrm {e}}^2-16\,{\mathrm {e}}^6+4\,{\mathrm {e}}^8+36}{{\left (x-1\right )}^2}-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.28, size = 32, normalized size = 1.28 \begin {gather*} - x - \frac {- 4 e^{8} - 40 e^{4} - 36 + 48 e^{2} + 16 e^{6}}{x^{2} - 2 x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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