Optimal. Leaf size=22 \[ 25+\frac {1}{3 \left (x+\log \left (\frac {1}{5} (3+x-\log (x))\right )\right )} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.24, antiderivative size = 20, normalized size of antiderivative = 0.91, number of steps
used = 3, number of rules used = 3, integrand size = 94, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {6820, 12, 6818}
\begin {gather*} \frac {1}{3 \left (x+\log \left (\frac {1}{5} (x-\log (x)+3)\right )\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1-4 x-x^2+x \log (x)}{3 x (3+x-\log (x)) \left (x+\log \left (\frac {1}{5} (3+x-\log (x))\right )\right )^2} \, dx\\ &=\frac {1}{3} \int \frac {1-4 x-x^2+x \log (x)}{x (3+x-\log (x)) \left (x+\log \left (\frac {1}{5} (3+x-\log (x))\right )\right )^2} \, dx\\ &=\frac {1}{3 \left (x+\log \left (\frac {1}{5} (3+x-\log (x))\right )\right )}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 20, normalized size = 0.91 \begin {gather*} \frac {1}{3 \left (x+\log \left (\frac {1}{5} (3+x-\log (x))\right )\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.13, size = 21, normalized size = 0.95
method | result | size |
risch | \(\frac {1}{3 \ln \left (-\frac {\ln \left (x \right )}{5}+\frac {3}{5}+\frac {x}{5}\right )+3 x}\) | \(17\) |
default | \(-\frac {1}{3 \left (\ln \left (5\right )-x -\ln \left (-\ln \left (x \right )+3+x \right )\right )}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.50, size = 18, normalized size = 0.82 \begin {gather*} \frac {1}{3 \, {\left (x - \log \left (5\right ) + \log \left (x - \log \left (x\right ) + 3\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.38, size = 16, normalized size = 0.73 \begin {gather*} \frac {1}{3 \, {\left (x + \log \left (\frac {1}{5} \, x - \frac {1}{5} \, \log \left (x\right ) + \frac {3}{5}\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.09, size = 19, normalized size = 0.86 \begin {gather*} \frac {1}{3 x + 3 \log {\left (\frac {x}{5} - \frac {\log {\left (x \right )}}{5} + \frac {3}{5} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.43, size = 18, normalized size = 0.82 \begin {gather*} \frac {1}{3 \, {\left (x - \log \left (5\right ) + \log \left (x - \log \left (x\right ) + 3\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 9.37, size = 18, normalized size = 0.82 \begin {gather*} \frac {1}{3\,\left (x+\ln \left (\frac {x}{5}-\frac {\ln \left (x\right )}{5}+\frac {3}{5}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________