Optimal. Leaf size=16 \[ \frac {2 x}{3}-\frac {1}{9} \log (2+3 x) \]
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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 = {45}
\begin {gather*} \frac {2 x}{3}-\frac {1}{9} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
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 \begin {gather*} \frac {1}{9} (4+6 x-\log (2+3 x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 13, normalized size = 0.81
method | result | size |
default | \(\frac {2 x}{3}-\frac {\ln \left (2+3 x \right )}{9}\) | \(13\) |
norman | \(\frac {2 x}{3}-\frac {\ln \left (2+3 x \right )}{9}\) | \(13\) |
meijerg | \(-\frac {\ln \left (1+\frac {3 x}{2}\right )}{9}+\frac {2 x}{3}\) | \(13\) |
risch | \(\frac {2 x}{3}-\frac {\ln \left (2+3 x \right )}{9}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 2.95, size = 12, normalized size = 0.75 \begin {gather*} \frac {2}{3} \, x - \frac {1}{9} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.78, size = 12, normalized size = 0.75 \begin {gather*} \frac {2}{3} \, x - \frac {1}{9} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 12, normalized size = 0.75 \begin {gather*} \frac {2 x}{3} - \frac {\log {\left (3 x + 2 \right )}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 13, normalized size = 0.81 \begin {gather*} \frac {2}{3} \, x - \frac {1}{9} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
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 \begin {gather*} \frac {2\,x}{3}-\frac {\ln \left (x+\frac {2}{3}\right )}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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