Optimal. Leaf size=19 \[ \frac {e^x}{x^2 \left (2+e^{176 x/3}+x\right )^2} \]
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Rubi [F] time = 1.93, 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 {e^{179 x/3} (-6-349 x)+e^x \left (-12-6 x+3 x^2\right )}{24 x^3+3 e^{176 x} x^3+36 x^4+18 x^5+3 x^6+e^{352 x/3} \left (18 x^3+9 x^4\right )+e^{176 x/3} \left (36 x^3+36 x^4+9 x^5\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 {e^x \left (-12-6 x+3 x^2-e^{176 x/3} (6+349 x)\right )}{3 x^3 \left (2+e^{176 x/3}+x\right )^3} \, dx\\ &=\frac {1}{3} \int \frac {e^x \left (-12-6 x+3 x^2-e^{176 x/3} (6+349 x)\right )}{x^3 \left (2+e^{176 x/3}+x\right )^3} \, dx\\ &=\frac {1}{3} \int \left (\frac {2 e^x (349+176 x)}{x^2 \left (2+e^{176 x/3}+x\right )^3}-\frac {e^x (6+349 x)}{x^3 \left (2+e^{176 x/3}+x\right )^2}\right ) \, dx\\ &=-\left (\frac {1}{3} \int \frac {e^x (6+349 x)}{x^3 \left (2+e^{176 x/3}+x\right )^2} \, dx\right )+\frac {2}{3} \int \frac {e^x (349+176 x)}{x^2 \left (2+e^{176 x/3}+x\right )^3} \, dx\\ &=-\left (\frac {1}{3} \int \left (\frac {6 e^x}{x^3 \left (2+e^{176 x/3}+x\right )^2}+\frac {349 e^x}{x^2 \left (2+e^{176 x/3}+x\right )^2}\right ) \, dx\right )+\frac {2}{3} \int \left (\frac {349 e^x}{x^2 \left (2+e^{176 x/3}+x\right )^3}+\frac {176 e^x}{x \left (2+e^{176 x/3}+x\right )^3}\right ) \, dx\\ &=-\left (2 \int \frac {e^x}{x^3 \left (2+e^{176 x/3}+x\right )^2} \, dx\right )-\frac {349}{3} \int \frac {e^x}{x^2 \left (2+e^{176 x/3}+x\right )^2} \, dx+\frac {352}{3} \int \frac {e^x}{x \left (2+e^{176 x/3}+x\right )^3} \, dx+\frac {698}{3} \int \frac {e^x}{x^2 \left (2+e^{176 x/3}+x\right )^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.38, size = 19, normalized size = 1.00 \begin {gather*} \frac {e^x}{x^2 \left (2+e^{176 x/3}+x\right )^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.71, size = 42, normalized size = 2.21 \begin {gather*} \frac {e^{x}}{x^{4} + 4 \, x^{3} + x^{2} e^{\left (\frac {352}{3} \, x\right )} + 4 \, x^{2} + 2 \, {\left (x^{3} + 2 \, x^{2}\right )} e^{\left (\frac {176}{3} \, x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 16, normalized size = 0.84
method | result | size |
risch | \(\frac {{\mathrm e}^{x}}{x^{2} \left ({\mathrm e}^{\frac {176 x}{3}}+x +2\right )^{2}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.21, size = 42, normalized size = 2.21 \begin {gather*} \frac {e^{x}}{x^{4} + 4 \, x^{3} + x^{2} e^{\left (\frac {352}{3} \, x\right )} + 4 \, x^{2} + 2 \, {\left (x^{3} + 2 \, x^{2}\right )} e^{\left (\frac {176}{3} \, x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int -\frac {{\mathrm {e}}^x\,\left (-3\,x^2+6\,x+12\right )+{\mathrm {e}}^{\frac {176\,x}{3}}\,{\mathrm {e}}^x\,\left (349\,x+6\right )}{{\mathrm {e}}^{\frac {352\,x}{3}}\,\left (9\,x^4+18\,x^3\right )+3\,x^3\,{\mathrm {e}}^{176\,x}+{\mathrm {e}}^{\frac {176\,x}{3}}\,\left (9\,x^5+36\,x^4+36\,x^3\right )+24\,x^3+36\,x^4+18\,x^5+3\,x^6} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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