Integrand size = 7, antiderivative size = 10 \[ \int \frac {1}{2+3 x} \, dx=\frac {1}{3} \log (2+3 x) \]
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Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {31} \[ \int \frac {1}{2+3 x} \, dx=\frac {1}{3} \log (3 x+2) \]
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Rule 31
Rubi steps \begin{align*} \text {integral}& = \frac {1}{3} \log (2+3 x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \frac {1}{2+3 x} \, dx=\frac {1}{3} \log (2+3 x) \]
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Time = 0.80 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.70
method | result | size |
parallelrisch | \(\frac {\ln \left (x +\frac {2}{3}\right )}{3}\) | \(7\) |
default | \(\frac {\ln \left (3 x +2\right )}{3}\) | \(9\) |
norman | \(\frac {\ln \left (3 x +2\right )}{3}\) | \(9\) |
meijerg | \(\frac {\ln \left (1+\frac {3 x}{2}\right )}{3}\) | \(9\) |
risch | \(\frac {\ln \left (3 x +2\right )}{3}\) | \(9\) |
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none
Time = 0.25 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {1}{2+3 x} \, dx=\frac {1}{3} \, \log \left (3 \, x + 2\right ) \]
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Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.70 \[ \int \frac {1}{2+3 x} \, dx=\frac {\log {\left (3 x + 2 \right )}}{3} \]
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none
Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {1}{2+3 x} \, dx=\frac {1}{3} \, \log \left (3 \, x + 2\right ) \]
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none
Time = 0.29 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.90 \[ \int \frac {1}{2+3 x} \, dx=\frac {1}{3} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.60 \[ \int \frac {1}{2+3 x} \, dx=\frac {\ln \left (x+\frac {2}{3}\right )}{3} \]
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