Optimal. Leaf size=17 \[ \log \left (5-e^{-x}-e^{8 x}\right ) \]
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Rubi [A] time = 0.14, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2282, 6742, 1587} \begin {gather*} \log \left (-5 e^x+e^{9 x}+1\right )-x \end {gather*}
Antiderivative was successfully verified.
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Rule 1587
Rule 2282
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\operatorname {Subst}\left (\int \frac {-1+8 x^9}{x \left (1-5 x+x^9\right )} \, dx,x,e^x\right )\\ &=\operatorname {Subst}\left (\int \left (-\frac {1}{x}+\frac {-5+9 x^8}{1-5 x+x^9}\right ) \, dx,x,e^x\right )\\ &=-x+\operatorname {Subst}\left (\int \frac {-5+9 x^8}{1-5 x+x^9} \, dx,x,e^x\right )\\ &=-x+\log \left (1-5 e^x+e^{9 x}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 17, normalized size = 1.00 \begin {gather*} -x+\log \left (1-5 e^x+e^{9 x}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 17, normalized size = 1.00 \begin {gather*} 8 \, x + \log \left (-5 \, e^{\left (-8 \, x\right )} + e^{\left (-9 \, x\right )} + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 16, normalized size = 0.94 \begin {gather*} -x + \log \left ({\left | e^{\left (9 \, x\right )} - 5 \, e^{x} + 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 12, normalized size = 0.71
method | result | size |
derivativedivides | \(\ln \left ({\mathrm e}^{8 x}+{\mathrm e}^{-x}-5\right )\) | \(12\) |
default | \(\ln \left ({\mathrm e}^{8 x}+{\mathrm e}^{-x}-5\right )\) | \(12\) |
risch | \(8 x +\ln \left ({\mathrm e}^{-9 x}-5 \,{\mathrm e}^{-8 x}+1\right )\) | \(18\) |
norman | \(8 x +\ln \left ({\mathrm e}^{-9 x}-5 \,{\mathrm e}^{-8 x}+1\right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 11, normalized size = 0.65 \begin {gather*} \log \left (e^{\left (8 \, x\right )} + e^{\left (-x\right )} - 5\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 15, normalized size = 0.88 \begin {gather*} \ln \left ({\mathrm {e}}^{9\,x}-5\,{\mathrm {e}}^x+1\right )-x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 19, normalized size = 1.12 \begin {gather*} 8 x + \log {\left (1 - 5 e^{- 8 x} + e^{- 9 x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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