Integrand size = 19, antiderivative size = 19 \[ \int \frac {3-2 e^{x/3} x}{3 x} \, dx=\log \left (e^{-2 e^{x/3}} \left (\frac {5}{86}+e\right ) x\right ) \]
[Out]
Time = 0.01 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {12, 14, 2225} \[ \int \frac {3-2 e^{x/3} x}{3 x} \, dx=\log (x)-2 e^{x/3} \]
[In]
[Out]
Rule 12
Rule 14
Rule 2225
Rubi steps \begin{align*} \text {integral}& = \frac {1}{3} \int \frac {3-2 e^{x/3} x}{x} \, dx \\ & = \frac {1}{3} \int \left (-2 e^{x/3}+\frac {3}{x}\right ) \, dx \\ & = \log (x)-\frac {2}{3} \int e^{x/3} \, dx \\ & = -2 e^{x/3}+\log (x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63 \[ \int \frac {3-2 e^{x/3} x}{3 x} \, dx=-2 e^{x/3}+\log (x) \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.53
method | result | size |
norman | \(-2 \,{\mathrm e}^{\frac {x}{3}}+\ln \left (x \right )\) | \(10\) |
risch | \(-2 \,{\mathrm e}^{\frac {x}{3}}+\ln \left (x \right )\) | \(10\) |
parallelrisch | \(-2 \,{\mathrm e}^{\frac {x}{3}}+\ln \left (x \right )\) | \(10\) |
parts | \(-2 \,{\mathrm e}^{\frac {x}{3}}+\ln \left (x \right )\) | \(10\) |
derivativedivides | \(\ln \left (\frac {x}{3}\right )-2 \,{\mathrm e}^{\frac {x}{3}}\) | \(12\) |
default | \(\ln \left (\frac {x}{3}\right )-2 \,{\mathrm e}^{\frac {x}{3}}\) | \(12\) |
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.47 \[ \int \frac {3-2 e^{x/3} x}{3 x} \, dx=-2 \, e^{\left (\frac {1}{3} \, x\right )} + \log \left (x\right ) \]
[In]
[Out]
Time = 0.04 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.42 \[ \int \frac {3-2 e^{x/3} x}{3 x} \, dx=- 2 e^{\frac {x}{3}} + \log {\left (x \right )} \]
[In]
[Out]
none
Time = 0.21 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.47 \[ \int \frac {3-2 e^{x/3} x}{3 x} \, dx=-2 \, e^{\left (\frac {1}{3} \, x\right )} + \log \left (x\right ) \]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.58 \[ \int \frac {3-2 e^{x/3} x}{3 x} \, dx=-2 \, e^{\left (\frac {1}{3} \, x\right )} + \log \left (\frac {1}{3} \, x\right ) \]
[In]
[Out]
Time = 0.05 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.47 \[ \int \frac {3-2 e^{x/3} x}{3 x} \, dx=\ln \left (x\right )-2\,{\mathrm {e}}^{x/3} \]
[In]
[Out]