Optimal. Leaf size=22 \[ 4+x-x^2 \left (2+\frac {1}{25} \left (5+e^4\right )^4+x\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 34, normalized size of antiderivative = 1.55, number of steps used = 6, number of rules used = 2, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {6, 12} \begin {gather*} -x^3-\frac {1}{25} \left (675+500 e^4+150 e^8+20 e^{12}+e^{16}\right ) x^2+x \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1}{25} \left (25-300 e^8 x-40 e^{12} x-2 e^{16} x+\left (-1350-1000 e^4\right ) x-75 x^2\right ) \, dx\\ &=\int \frac {1}{25} \left (25-2 e^{16} x+\left (-1350-1000 e^4\right ) x+\left (-300 e^8-40 e^{12}\right ) x-75 x^2\right ) \, dx\\ &=\int \frac {1}{25} \left (25+\left (-300 e^8-40 e^{12}\right ) x+\left (-1350-1000 e^4-2 e^{16}\right ) x-75 x^2\right ) \, dx\\ &=\int \frac {1}{25} \left (25+\left (-1350-1000 e^4-300 e^8-40 e^{12}-2 e^{16}\right ) x-75 x^2\right ) \, dx\\ &=\frac {1}{25} \int \left (25+\left (-1350-1000 e^4-300 e^8-40 e^{12}-2 e^{16}\right ) x-75 x^2\right ) \, dx\\ &=x-\frac {1}{25} \left (675+500 e^4+150 e^8+20 e^{12}+e^{16}\right ) x^2-x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 34, normalized size = 1.55 \begin {gather*} x-\frac {1}{25} \left (675+500 e^4+150 e^8+20 e^{12}+e^{16}\right ) x^2-x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.54, size = 40, normalized size = 1.82 \begin {gather*} -x^{3} - \frac {1}{25} \, x^{2} e^{16} - \frac {4}{5} \, x^{2} e^{12} - 6 \, x^{2} e^{8} - 20 \, x^{2} e^{4} - 27 \, x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.14, size = 40, normalized size = 1.82 \begin {gather*} -x^{3} - \frac {1}{25} \, x^{2} e^{16} - \frac {4}{5} \, x^{2} e^{12} - 6 \, x^{2} e^{8} - 20 \, x^{2} e^{4} - 27 \, x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 36, normalized size = 1.64
method | result | size |
norman | \(x +\left (-\frac {{\mathrm e}^{16}}{25}-\frac {4 \,{\mathrm e}^{12}}{5}-6 \,{\mathrm e}^{8}-20 \,{\mathrm e}^{4}-27\right ) x^{2}-x^{3}\) | \(36\) |
gosper | \(-\frac {x \left (x \,{\mathrm e}^{16}+20 x \,{\mathrm e}^{12}+150 x \,{\mathrm e}^{8}+500 x \,{\mathrm e}^{4}+25 x^{2}+675 x -25\right )}{25}\) | \(39\) |
risch | \(-\frac {x^{2} {\mathrm e}^{16}}{25}-\frac {4 x^{2} {\mathrm e}^{12}}{5}-6 x^{2} {\mathrm e}^{8}-20 x^{2} {\mathrm e}^{4}-x^{3}-27 x^{2}+x\) | \(41\) |
default | \(-\frac {x^{2} {\mathrm e}^{16}}{25}-\frac {4 x^{2} {\mathrm e}^{12}}{5}-6 x^{2} {\mathrm e}^{8}-20 x^{2} {\mathrm e}^{4}-x^{3}-27 x^{2}+x\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.36, size = 40, normalized size = 1.82 \begin {gather*} -x^{3} - \frac {1}{25} \, x^{2} e^{16} - \frac {4}{5} \, x^{2} e^{12} - 6 \, x^{2} e^{8} - 20 \, x^{2} e^{4} - 27 \, x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 30, normalized size = 1.36 \begin {gather*} -x^3+\left (-20\,{\mathrm {e}}^4-6\,{\mathrm {e}}^8-\frac {4\,{\mathrm {e}}^{12}}{5}-\frac {{\mathrm {e}}^{16}}{25}-27\right )\,x^2+x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 32, normalized size = 1.45 \begin {gather*} - x^{3} + x^{2} \left (- \frac {e^{16}}{25} - \frac {4 e^{12}}{5} - 6 e^{8} - 20 e^{4} - 27\right ) + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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