Optimal. Leaf size=22 \[ -3+e^{-1+3 e^3+e^{\frac {2}{\frac {95}{9}+x}}} \]
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Rubi [A] time = 0.32, antiderivative size = 20, normalized size of antiderivative = 0.91, number of steps used = 6, number of rules used = 5, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.116, Rules used = {12, 27, 6715, 2282, 2194} \begin {gather*} e^{e^{\frac {18}{9 x+95}}-1+3 e^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 2194
Rule 2282
Rule 6715
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (162 \int \frac {e^{-1+3 e^3+e^{\frac {18}{95+9 x}}+\frac {18}{95+9 x}}}{9025+1710 x+81 x^2} \, dx\right )\\ &=-\left (162 \int \frac {e^{-1+3 e^3+e^{\frac {18}{95+9 x}}+\frac {18}{95+9 x}}}{(95+9 x)^2} \, dx\right )\\ &=-\left (18 \operatorname {Subst}\left (\int \frac {e^{-1+3 e^3+e^{18/x}+\frac {18}{x}}}{x^2} \, dx,x,95+9 x\right )\right )\\ &=18 \operatorname {Subst}\left (\int e^{-1+3 e^3+e^{18 x}+18 x} \, dx,x,\frac {1}{95+9 x}\right )\\ &=\operatorname {Subst}\left (\int e^{-1+3 e^3+x} \, dx,x,e^{\frac {18}{95+9 x}}\right )\\ &=e^{-1+3 e^3+e^{\frac {18}{95+9 x}}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 20, normalized size = 0.91 \begin {gather*} e^{-1+3 e^3+e^{\frac {18}{95+9 x}}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.64, size = 49, normalized size = 2.23 \begin {gather*} e^{\left (\frac {3 \, {\left (9 \, x + 95\right )} e^{3} + {\left (9 \, x + 95\right )} e^{\left (\frac {18}{9 \, x + 95}\right )} - 9 \, x - 77}{9 \, x + 95} - \frac {18}{9 \, x + 95}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.27, size = 54, normalized size = 2.45 \begin {gather*} e^{\left (\frac {855 \, x e^{\left (\frac {18}{9 \, x + 95}\right )} - 162 \, x + 9025 \, e^{\left (\frac {18}{9 \, x + 95}\right )}}{95 \, {\left (9 \, x + 95\right )}} - \frac {18}{9 \, x + 95} + 3 \, e^{3} - \frac {77}{95}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.48, size = 18, normalized size = 0.82
method | result | size |
risch | \({\mathrm e}^{3 \,{\mathrm e}^{3}+{\mathrm e}^{\frac {18}{9 x +95}}-1}\) | \(18\) |
norman | \(\frac {95 \,{\mathrm e}^{3 \,{\mathrm e}^{3}} {\mathrm e}^{{\mathrm e}^{\frac {18}{9 x +95}}-1}+9 \,{\mathrm e}^{3 \,{\mathrm e}^{3}} x \,{\mathrm e}^{{\mathrm e}^{\frac {18}{9 x +95}}-1}}{9 x +95}\) | \(51\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 17, normalized size = 0.77 \begin {gather*} e^{\left (3 \, e^{3} + e^{\left (\frac {18}{9 \, x + 95}\right )} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.92, size = 19, normalized size = 0.86 \begin {gather*} {\mathrm {e}}^{3\,{\mathrm {e}}^3}\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {18}{9\,x+95}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.40, size = 17, normalized size = 0.77 \begin {gather*} e^{e^{\frac {18}{9 x + 95}} - 1} e^{3 e^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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