Optimal. Leaf size=28 \[ \frac {x}{3-x \left (3+\frac {e^{x+17 x^2}+x^3}{x}\right )} \]
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Rubi [F]
time = 0.85, 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 {3+2 x^3+e^{x+17 x^2} \left (-1+x+34 x^2\right )}{9+e^{2 x+34 x^2}-18 x+9 x^2-6 x^3+6 x^4+x^6+e^{x+17 x^2} \left (-6+6 x+2 x^3\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3+2 x^3+e^{x+17 x^2} \left (-1+x+34 x^2\right )}{\left (3-e^{x+17 x^2}-3 x-x^3\right )^2} \, dx\\ &=\int \left (\frac {-1+x+34 x^2}{-3+e^{x+17 x^2}+3 x+x^3}-\frac {x \left (-6-99 x+99 x^2+x^3+34 x^4\right )}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2}\right ) \, dx\\ &=\int \frac {-1+x+34 x^2}{-3+e^{x+17 x^2}+3 x+x^3} \, dx-\int \frac {x \left (-6-99 x+99 x^2+x^3+34 x^4\right )}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2} \, dx\\ &=-\int \left (-\frac {6 x}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2}-\frac {99 x^2}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2}+\frac {99 x^3}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2}+\frac {x^4}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2}+\frac {34 x^5}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2}\right ) \, dx+\int \left (-\frac {1}{-3+e^{x+17 x^2}+3 x+x^3}+\frac {x}{-3+e^{x+17 x^2}+3 x+x^3}+\frac {34 x^2}{-3+e^{x+17 x^2}+3 x+x^3}\right ) \, dx\\ &=6 \int \frac {x}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2} \, dx-34 \int \frac {x^5}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2} \, dx+34 \int \frac {x^2}{-3+e^{x+17 x^2}+3 x+x^3} \, dx+99 \int \frac {x^2}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2} \, dx-99 \int \frac {x^3}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2} \, dx-\int \frac {x^4}{\left (-3+e^{x+17 x^2}+3 x+x^3\right )^2} \, dx-\int \frac {1}{-3+e^{x+17 x^2}+3 x+x^3} \, dx+\int \frac {x}{-3+e^{x+17 x^2}+3 x+x^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 2.97, size = 22, normalized size = 0.79 \begin {gather*} -\frac {x}{-3+e^{x+17 x^2}+3 x+x^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 22, normalized size = 0.79
method | result | size |
risch | \(-\frac {x}{x^{3}+{\mathrm e}^{x \left (17 x +1\right )}+3 x -3}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 21, normalized size = 0.75 \begin {gather*} -\frac {x}{x^{3} + 3 \, x + e^{\left (17 \, x^{2} + x\right )} - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.50, size = 21, normalized size = 0.75 \begin {gather*} -\frac {x}{x^{3} + 3 \, x + e^{\left (17 \, x^{2} + x\right )} - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 20, normalized size = 0.71 \begin {gather*} - \frac {x}{x^{3} + 3 x + e^{x} e^{17 x^{2}} - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 21, normalized size = 0.75 \begin {gather*} -\frac {x}{x^{3} + 3 \, x + e^{\left (17 \, x^{2} + x\right )} - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.82, size = 21, normalized size = 0.75 \begin {gather*} -\frac {x}{3\,x+{\mathrm {e}}^{17\,x^2+x}+x^3-3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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