Optimal. Leaf size=16 \[ \frac {2 x}{3}-\frac {1}{9} \log (3 x+2) \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {43} \[ \frac {2 x}{3}-\frac {1}{9} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {1+2 x}{2+3 x} \, dx &=\int \left (\frac {2}{3}-\frac {1}{3 (2+3 x)}\right ) \, dx\\ &=\frac {2 x}{3}-\frac {1}{9} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.06 \[ \frac {1}{9} (6 x-\log (3 x+2)+4) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 12, normalized size = 0.75 \[ \frac {2}{3} \, x - \frac {1}{9} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.00, size = 13, normalized size = 0.81 \[ \frac {2}{3} \, x - \frac {1}{9} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.81 \[ \frac {2 x}{3}-\frac {\ln \left (3 x +2\right )}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 12, normalized size = 0.75 \[ \frac {2}{3} \, x - \frac {1}{9} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.14, size = 10, normalized size = 0.62 \[ \frac {2\,x}{3}-\frac {\ln \left (x+\frac {2}{3}\right )}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 12, normalized size = 0.75 \[ \frac {2 x}{3} - \frac {\log {\left (3 x + 2 \right )}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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