Optimal. Leaf size=21 \[ 3 \left (5+\log \left (-1+x \log (x)+e^4 \log \left (\frac {3}{2}+x\right )\right )\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.21, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 57, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.035, Rules used = {6741, 6684} \begin {gather*} 3 \log \left (-x \log (x)-e^4 \log \left (x+\frac {3}{2}\right )+1\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6684
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-9 \left (1+\frac {2 e^4}{3}\right )-6 x-(9+6 x) \log (x)}{(3+2 x) \left (1-x \log (x)-e^4 \log \left (\frac {3}{2}+x\right )\right )} \, dx\\ &=3 \log \left (1-x \log (x)-e^4 \log \left (\frac {3}{2}+x\right )\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.48, size = 21, normalized size = 1.00 \begin {gather*} 3 \log \left (1-x \log (x)-e^4 \log \left (\frac {3}{2}+x\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.80, size = 16, normalized size = 0.76 \begin {gather*} 3 \, \log \left (e^{4} \log \left (x + \frac {3}{2}\right ) + x \log \relax (x) - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.40, size = 24, normalized size = 1.14 \begin {gather*} 3 \, \log \left (-e^{4} \log \relax (2) + e^{4} \log \left (2 \, x + 3\right ) + x \log \relax (x) - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.25, size = 17, normalized size = 0.81
method | result | size |
norman | \(3 \ln \left ({\mathrm e}^{4} \ln \left (x +\frac {3}{2}\right )+x \ln \relax (x )-1\right )\) | \(17\) |
risch | \(3 \ln \left (\ln \left (x +\frac {3}{2}\right )+\left (x \ln \relax (x )-1\right ) {\mathrm e}^{-4}\right )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.56, size = 29, normalized size = 1.38 \begin {gather*} 3 \, \log \left (-{\left (e^{4} \log \relax (2) - e^{4} \log \left (2 \, x + 3\right ) - x \log \relax (x) + 1\right )} e^{\left (-4\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.01, size = 16, normalized size = 0.76 \begin {gather*} 3\,\ln \left (\ln \left (x+\frac {3}{2}\right )\,{\mathrm {e}}^4+x\,\ln \relax (x)-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.41, size = 19, normalized size = 0.90 \begin {gather*} 3 \log {\left (\frac {x \log {\relax (x )} - 1}{e^{4}} + \log {\left (x + \frac {3}{2} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________