Optimal. Leaf size=27 \[ \frac {16}{\left (e^{2 x-x (5+x) (4+x (6+x))}-x\right )^2} \]
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Rubi [F] time = 4.40, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {32+e^{-18 x-34 x^2-11 x^3-x^4} \left (576+2176 x+1056 x^2+128 x^3\right )}{e^{-54 x-102 x^2-33 x^3-3 x^4}-3 e^{-36 x-68 x^2-22 x^3-2 x^4} x+3 e^{-18 x-34 x^2-11 x^3-x^4} x^2-x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {32 e^{2 x \left (18+34 x+11 x^2+x^3\right )} \left (18+e^{x \left (18+34 x+11 x^2+x^3\right )}+68 x+33 x^2+4 x^3\right )}{\left (1-e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^3} \, dx\\ &=32 \int \frac {e^{2 x \left (18+34 x+11 x^2+x^3\right )} \left (18+e^{x \left (18+34 x+11 x^2+x^3\right )}+68 x+33 x^2+4 x^3\right )}{\left (1-e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^3} \, dx\\ &=32 \int \left (-\frac {e^{2 x \left (18+34 x+11 x^2+x^3\right )}}{x \left (-1+e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^2}-\frac {e^{2 x \left (18+34 x+11 x^2+x^3\right )} \left (1+18 x+68 x^2+33 x^3+4 x^4\right )}{x \left (-1+e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^3}\right ) \, dx\\ &=-\left (32 \int \frac {e^{2 x \left (18+34 x+11 x^2+x^3\right )}}{x \left (-1+e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^2} \, dx\right )-32 \int \frac {e^{2 x \left (18+34 x+11 x^2+x^3\right )} \left (1+18 x+68 x^2+33 x^3+4 x^4\right )}{x \left (-1+e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^3} \, dx\\ &=-\left (32 \int \frac {e^{2 x \left (18+34 x+11 x^2+x^3\right )}}{x \left (-1+e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^2} \, dx\right )-32 \int \left (\frac {18 e^{2 x \left (18+34 x+11 x^2+x^3\right )}}{\left (-1+e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^3}+\frac {e^{2 x \left (18+34 x+11 x^2+x^3\right )}}{x \left (-1+e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^3}+\frac {68 e^{2 x \left (18+34 x+11 x^2+x^3\right )} x}{\left (-1+e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^3}+\frac {33 e^{2 x \left (18+34 x+11 x^2+x^3\right )} x^2}{\left (-1+e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^3}+\frac {4 e^{2 x \left (18+34 x+11 x^2+x^3\right )} x^3}{\left (-1+e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^3}\right ) \, dx\\ &=-\left (32 \int \frac {e^{2 x \left (18+34 x+11 x^2+x^3\right )}}{x \left (-1+e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^3} \, dx\right )-32 \int \frac {e^{2 x \left (18+34 x+11 x^2+x^3\right )}}{x \left (-1+e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^2} \, dx-128 \int \frac {e^{2 x \left (18+34 x+11 x^2+x^3\right )} x^3}{\left (-1+e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^3} \, dx-576 \int \frac {e^{2 x \left (18+34 x+11 x^2+x^3\right )}}{\left (-1+e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^3} \, dx-1056 \int \frac {e^{2 x \left (18+34 x+11 x^2+x^3\right )} x^2}{\left (-1+e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^3} \, dx-2176 \int \frac {e^{2 x \left (18+34 x+11 x^2+x^3\right )} x}{\left (-1+e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.80, size = 43, normalized size = 1.59 \begin {gather*} \frac {16 e^{2 x \left (18+34 x+11 x^2+x^3\right )}}{\left (-1+e^{x \left (18+34 x+11 x^2+x^3\right )} x\right )^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 51, normalized size = 1.89 \begin {gather*} \frac {16}{x^{2} - 2 \, x e^{\left (-x^{4} - 11 \, x^{3} - 34 \, x^{2} - 18 \, x\right )} + e^{\left (-2 \, x^{4} - 22 \, x^{3} - 68 \, x^{2} - 36 \, x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.92, size = 51, normalized size = 1.89 \begin {gather*} \frac {16}{x^{2} - 2 \, x e^{\left (-x^{4} - 11 \, x^{3} - 34 \, x^{2} - 18 \, x\right )} + e^{\left (-2 \, x^{4} - 22 \, x^{3} - 68 \, x^{2} - 36 \, x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.13, size = 26, normalized size = 0.96
method | result | size |
risch | \(\frac {16}{\left (x -{\mathrm e}^{-x \left (x^{3}+11 x^{2}+34 x +18\right )}\right )^{2}}\) | \(26\) |
norman | \(\frac {16}{\left (x -{\mathrm e}^{-x^{4}-11 x^{3}-34 x^{2}-18 x}\right )^{2}}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.63, size = 71, normalized size = 2.63 \begin {gather*} \frac {16 \, e^{\left (2 \, x^{4} + 22 \, x^{3} + 68 \, x^{2} + 36 \, x\right )}}{x^{2} e^{\left (2 \, x^{4} + 22 \, x^{3} + 68 \, x^{2} + 36 \, x\right )} - 2 \, x e^{\left (x^{4} + 11 \, x^{3} + 34 \, x^{2} + 18 \, x\right )} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.60, size = 56, normalized size = 2.07 \begin {gather*} \frac {16}{x^2+{\mathrm {e}}^{-36\,x}\,{\mathrm {e}}^{-2\,x^4}\,{\mathrm {e}}^{-22\,x^3}\,{\mathrm {e}}^{-68\,x^2}-2\,x\,{\mathrm {e}}^{-18\,x}\,{\mathrm {e}}^{-x^4}\,{\mathrm {e}}^{-11\,x^3}\,{\mathrm {e}}^{-34\,x^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.23, size = 49, normalized size = 1.81 \begin {gather*} \frac {16}{x^{2} - 2 x e^{- x^{4} - 11 x^{3} - 34 x^{2} - 18 x} + e^{- 2 x^{4} - 22 x^{3} - 68 x^{2} - 36 x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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