Optimal. Leaf size=25 \[ \frac {16}{\left (1-e^{e^9}+9 \left (e^3-x\right )\right ) x} \]
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Rubi [A]
time = 0.11, antiderivative size = 24, normalized size of antiderivative = 0.96, number of steps
used = 5, number of rules used = 4, integrand size = 93, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {6, 1694, 12,
267} \begin {gather*} \frac {16}{\left (-9 x-e^{e^9}+9 e^3+1\right ) x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 267
Rule 1694
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-16-144 e^3+16 e^{e^9}+288 x}{e^{2 e^9} x^2+\left (1+81 e^6\right ) x^2-18 x^3+81 x^4+e^3 \left (18 x^2-162 x^3\right )+e^{e^9} \left (-2 x^2-18 e^3 x^2+18 x^3\right )} \, dx\\ &=\int \frac {-16-144 e^3+16 e^{e^9}+288 x}{\left (1+81 e^6+e^{2 e^9}\right ) x^2-18 x^3+81 x^4+e^3 \left (18 x^2-162 x^3\right )+e^{e^9} \left (-2 x^2-18 e^3 x^2+18 x^3\right )} \, dx\\ &=\text {Subst}\left (\int \frac {373248 x}{\left (1+18 e^3+81 e^6-2 e^{e^9}+e^{2 e^9}-18 e^{3+e^9}-324 x^2\right )^2} \, dx,x,\frac {1}{324} \left (-18-162 e^3+18 e^{e^9}\right )+x\right )\\ &=373248 \text {Subst}\left (\int \frac {x}{\left (1+18 e^3+81 e^6-2 e^{e^9}+e^{2 e^9}-18 e^{3+e^9}-324 x^2\right )^2} \, dx,x,\frac {1}{324} \left (-18-162 e^3+18 e^{e^9}\right )+x\right )\\ &=\frac {16}{\left (1+9 e^3-e^{e^9}-9 x\right ) x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 25, normalized size = 1.00 \begin {gather*} \frac {16}{x+9 e^3 x-e^{e^9} x-9 x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.43, size = 22, normalized size = 0.88
method | result | size |
gosper | \(\frac {16}{\left (-9 x +9 \,{\mathrm e}^{3}-{\mathrm e}^{{\mathrm e}^{9}}+1\right ) x}\) | \(22\) |
norman | \(\frac {16}{\left (-9 x +9 \,{\mathrm e}^{3}-{\mathrm e}^{{\mathrm e}^{9}}+1\right ) x}\) | \(22\) |
risch | \(\frac {16}{\left (-9 x +9 \,{\mathrm e}^{3}-{\mathrm e}^{{\mathrm e}^{9}}+1\right ) x}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 24, normalized size = 0.96 \begin {gather*} -\frac {16}{9 \, x^{2} - x {\left (9 \, e^{3} - e^{\left (e^{9}\right )} + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 23, normalized size = 0.92 \begin {gather*} -\frac {16}{9 \, x^{2} - 9 \, x e^{3} + x e^{\left (e^{9}\right )} - x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.43, size = 20, normalized size = 0.80 \begin {gather*} - \frac {16}{9 x^{2} + x \left (- 9 e^{3} - 1 + e^{e^{9}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F(-1)]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \text {Hanged} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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