Optimal. Leaf size=28 \[ 4-e^2+\frac {e^{3 x}}{-4+x}+\log \left (-x+\frac {x}{e^4}\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.29, antiderivative size = 17, normalized size of antiderivative = 0.61, number of steps used = 5, number of rules used = 4, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {1594, 27, 6742, 2197} \begin {gather*} \log (x)-\frac {e^{3 x}}{4-x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 27
Rule 1594
Rule 2197
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {16-8 x+x^2+e^{3 x} \left (-13 x+3 x^2\right )}{x \left (16-8 x+x^2\right )} \, dx\\ &=\int \frac {16-8 x+x^2+e^{3 x} \left (-13 x+3 x^2\right )}{(-4+x)^2 x} \, dx\\ &=\int \left (\frac {1}{x}+\frac {e^{3 x} (-13+3 x)}{(-4+x)^2}\right ) \, dx\\ &=\log (x)+\int \frac {e^{3 x} (-13+3 x)}{(-4+x)^2} \, dx\\ &=-\frac {e^{3 x}}{4-x}+\log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.10, size = 14, normalized size = 0.50 \begin {gather*} \frac {e^{3 x}}{-4+x}+\log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.63, size = 17, normalized size = 0.61 \begin {gather*} \frac {{\left (x - 4\right )} \log \relax (x) + e^{\left (3 \, x\right )}}{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 3.22, size = 19, normalized size = 0.68 \begin {gather*} \frac {x \log \relax (x) + e^{\left (3 \, x\right )} - 4 \, \log \relax (x)}{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 14, normalized size = 0.50
method | result | size |
norman | \(\frac {{\mathrm e}^{3 x}}{x -4}+\ln \relax (x )\) | \(14\) |
risch | \(\frac {{\mathrm e}^{3 x}}{x -4}+\ln \relax (x )\) | \(14\) |
derivativedivides | \(\ln \left (3 x \right )+\frac {3 \,{\mathrm e}^{3 x}}{3 x -12}\) | \(19\) |
default | \(\ln \left (3 x \right )+\frac {3 \,{\mathrm e}^{3 x}}{3 x -12}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {x e^{\left (3 \, x\right )}}{x^{2} - 8 \, x + 16} + \frac {13 \, e^{12} E_{2}\left (-3 \, x + 12\right )}{x - 4} + 3 \, \int \frac {{\left (x + 4\right )} e^{\left (3 \, x\right )}}{3 \, {\left (x^{3} - 12 \, x^{2} + 48 \, x - 64\right )}}\,{d x} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.08, size = 13, normalized size = 0.46 \begin {gather*} \ln \relax (x)+\frac {{\mathrm {e}}^{3\,x}}{x-4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, size = 10, normalized size = 0.36 \begin {gather*} \log {\relax (x )} + \frac {e^{3 x}}{x - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________