Optimal. Leaf size=13 \[ \log (3 x+2)-\log (x+1) \]
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Rubi [A] time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {616, 31} \[ \log (3 x+2)-\log (x+1) \]
Antiderivative was successfully verified.
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Rule 31
Rule 616
Rubi steps
\begin {align*} \int \frac {1}{2+5 x+3 x^2} \, dx &=3 \int \frac {1}{2+3 x} \, dx-3 \int \frac {1}{3+3 x} \, dx\\ &=-\log (1+x)+\log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \[ \log (3 x+2)-\log (x+1) \]
Antiderivative was successfully verified.
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fricas [A] time = 1.04, size = 13, normalized size = 1.00 \[ \log \left (3 \, x + 2\right ) - \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.51, size = 15, normalized size = 1.15 \[ \log \left ({\left | 3 \, x + 2 \right |}\right ) - \log \left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 14, normalized size = 1.08 \[ \ln \left (3 x +2\right )-\ln \left (x +1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 13, normalized size = 1.00 \[ \log \left (3 \, x + 2\right ) - \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 8, normalized size = 0.62 \[ -2\,\mathrm {atanh}\left (6\,x+5\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 10, normalized size = 0.77 \[ \log {\left (x + \frac {2}{3} \right )} - \log {\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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