Optimal. Leaf size=37 \[ 4+\log \left (\frac {x}{2 \left (-x+x^2 \left (-2+\log \left (\frac {x^2+\frac {1}{3} (x+\log (5))}{x}\right )\right )\right )}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.28, antiderivative size = 26, normalized size of antiderivative = 0.70, number of steps
used = 2, number of rules used = 2, integrand size = 100, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {6873, 6816}
\begin {gather*} -\log \left (2 x+x \left (-\log \left (x+\frac {\log (5)}{3 x}+\frac {1}{3}\right )\right )+1\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6816
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-2 x-3 x^2-3 \log (5)-\left (-x-3 x^2-\log (5)\right ) \log \left (\frac {x+3 x^2+\log (5)}{3 x}\right )}{\left (x+3 x^2+\log (5)\right ) \left (1+2 x-x \log \left (\frac {1}{3}+x+\frac {\log (5)}{3 x}\right )\right )} \, dx\\ &=-\log \left (1+2 x-x \log \left (\frac {1}{3}+x+\frac {\log (5)}{3 x}\right )\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [F]
time = 1.20, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 x+3 x^2+3 \log (5)+\left (-x-3 x^2-\log (5)\right ) \log \left (\frac {x+3 x^2+\log (5)}{3 x}\right )}{-x-5 x^2-6 x^3+(-1-2 x) \log (5)+\left (x^2+3 x^3+x \log (5)\right ) \log \left (\frac {x+3 x^2+\log (5)}{3 x}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 1.41, size = 26, normalized size = 0.70
method | result | size |
norman | \(-\ln \left (\ln \left (\frac {\ln \left (5\right )+3 x^{2}+x}{3 x}\right ) x -2 x -1\right )\) | \(26\) |
risch | \(-\ln \left (x \right )-\ln \left (\ln \left (\frac {\ln \left (5\right )+3 x^{2}+x}{3 x}\right )-\frac {2 x +1}{x}\right )\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.52, size = 38, normalized size = 1.03 \begin {gather*} -\log \left (x\right ) - \log \left (-\frac {x {\left (\log \left (3\right ) + 2\right )} - x \log \left (3 \, x^{2} + x + \log \left (5\right )\right ) + x \log \left (x\right ) + 1}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.40, size = 34, normalized size = 0.92 \begin {gather*} -\log \left (x\right ) - \log \left (\frac {x \log \left (\frac {3 \, x^{2} + x + \log \left (5\right )}{3 \, x}\right ) - 2 \, x - 1}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.19, size = 29, normalized size = 0.78 \begin {gather*} - \log {\left (x \right )} - \log {\left (\log {\left (\frac {x^{2} + \frac {x}{3} + \frac {\log {\left (5 \right )}}{3}}{x} \right )} + \frac {- 2 x - 1}{x} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.43, size = 27, normalized size = 0.73 \begin {gather*} -\log \left (-x \log \left (3 \, x^{2} + x + \log \left (5\right )\right ) + x \log \left (3 \, x\right ) + 2 \, x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 6.00, size = 35, normalized size = 0.95 \begin {gather*} -\ln \left (\frac {2\,x-x\,\ln \left (\frac {3\,x^2+x+\ln \left (5\right )}{3\,x}\right )+1}{x}\right )-\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________