Optimal. Leaf size=26 \[ 4-\log \left (e^{(-4+x)^2} \left (29-e^x\right ) (1-x) x\right ) \]
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Rubi [A] time = 0.66, antiderivative size = 31, normalized size of antiderivative = 1.19, number of steps used = 9, number of rules used = 7, integrand size = 57, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.123, Rules used = {6741, 6742, 2282, 36, 31, 29, 1620} \begin {gather*} -x^2+8 x-\log \left (29-e^x\right )-\log (1-x)-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 31
Rule 36
Rule 1620
Rule 2282
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-29+290 x-290 x^2+58 x^3+e^x \left (1-9 x+9 x^2-2 x^3\right )}{\left (29-e^x\right ) (1-x) x} \, dx\\ &=\int \left (-\frac {29}{-29+e^x}+\frac {1-9 x+9 x^2-2 x^3}{(-1+x) x}\right ) \, dx\\ &=-\left (29 \int \frac {1}{-29+e^x} \, dx\right )+\int \frac {1-9 x+9 x^2-2 x^3}{(-1+x) x} \, dx\\ &=-\left (29 \operatorname {Subst}\left (\int \frac {1}{(-29+x) x} \, dx,x,e^x\right )\right )+\int \left (7+\frac {1}{1-x}-\frac {1}{x}-2 x\right ) \, dx\\ &=7 x-x^2-\log (1-x)-\log (x)-\operatorname {Subst}\left (\int \frac {1}{-29+x} \, dx,x,e^x\right )+\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,e^x\right )\\ &=8 x-x^2-\log \left (29-e^x\right )-\log (1-x)-\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.09, size = 31, normalized size = 1.19 \begin {gather*} 8 x-x^2-\log \left (29-e^x\right )-\log (1-x)-\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 26, normalized size = 1.00 \begin {gather*} -x^{2} + 8 \, x - \log \left (x^{2} - x\right ) - \log \left (e^{x} - 29\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 26, normalized size = 1.00 \begin {gather*} -x^{2} + 8 \, x - \log \left (x - 1\right ) - \log \relax (x) - \log \left (e^{x} - 29\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 27, normalized size = 1.04
method | result | size |
norman | \(-x^{2}+8 x -\ln \relax (x )-\ln \left (x -1\right )-\ln \left ({\mathrm e}^{x}-29\right )\) | \(27\) |
risch | \(-x^{2}+8 x -\ln \left (x^{2}-x \right )-\ln \left ({\mathrm e}^{x}-29\right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.41, size = 26, normalized size = 1.00 \begin {gather*} -x^{2} + 8 \, x - \log \left (x - 1\right ) - \log \relax (x) - \log \left (e^{x} - 29\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 26, normalized size = 1.00 \begin {gather*} 8\,x-\ln \left (x-1\right )-\ln \left ({\mathrm {e}}^x-29\right )-\ln \relax (x)-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 19, normalized size = 0.73 \begin {gather*} - x^{2} + 8 x - \log {\left (x^{2} - x \right )} - \log {\left (e^{x} - 29 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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