Optimal. Leaf size=35 \[ -\frac {1}{5} (11-5 x) \log \left (-\frac {11-5 x}{76 x+5}\right )-\frac {861}{380} \log (76 x+5) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 35, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2486, 31} \[ -\frac {1}{5} (11-5 x) \log \left (-\frac {11-5 x}{76 x+5}\right )-\frac {861}{380} \log (76 x+5) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 31
Rule 2486
Rubi steps
\begin {align*} \int \log \left (\frac {-11+5 x}{5+76 x}\right ) \, dx &=-\frac {1}{5} (11-5 x) \log \left (-\frac {11-5 x}{5+76 x}\right )-\frac {861}{5} \int \frac {1}{5+76 x} \, dx\\ &=-\frac {1}{5} (11-5 x) \log \left (-\frac {11-5 x}{5+76 x}\right )-\frac {861}{380} \log (5+76 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 31, normalized size = 0.89 \[ \left (x-\frac {11}{5}\right ) \log \left (\frac {5 x-11}{76 x+5}\right )-\frac {861}{380} \log (76 x+5) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.50, size = 33, normalized size = 0.94 \[ x \log \left (\frac {5 \, x - 11}{76 \, x + 5}\right ) - \frac {5}{76} \, \log \left (76 \, x + 5\right ) - \frac {11}{5} \, \log \left (5 \, x - 11\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.19, size = 139, normalized size = 3.97 \[ -\frac {861 \, \log \left (\frac {\frac {5 \, {\left (\frac {5 \, {\left (5 \, x - 11\right )}}{76 \, x + 5} + 11\right )}}{\frac {76 \, {\left (5 \, x - 11\right )}}{76 \, x + 5} - 5} + 11}{\frac {76 \, {\left (\frac {5 \, {\left (5 \, x - 11\right )}}{76 \, x + 5} + 11\right )}}{\frac {76 \, {\left (5 \, x - 11\right )}}{76 \, x + 5} - 5} - 5}\right )}{76 \, {\left (\frac {76 \, {\left (5 \, x - 11\right )}}{76 \, x + 5} - 5\right )}} - \frac {861}{380} \, \log \left (\frac {{\left | 5 \, x - 11 \right |}}{{\left | 76 \, x + 5 \right |}}\right ) + \frac {861}{380} \, \log \left ({\left | \frac {76 \, {\left (5 \, x - 11\right )}}{76 \, x + 5} - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.17, size = 44, normalized size = 1.26 \[ \frac {861 \ln \left (-\frac {861}{76 x +5}\right )}{380}+\frac {\left (\frac {5}{76}-\frac {861}{76 \left (76 x +5\right )}\right ) \left (76 x +5\right ) \ln \left (\frac {5}{76}-\frac {861}{76 \left (76 x +5\right )}\right )}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.61, size = 33, normalized size = 0.94 \[ x \log \left (\frac {5 \, x - 11}{76 \, x + 5}\right ) - \frac {5}{76} \, \log \left (76 \, x + 5\right ) - \frac {11}{5} \, \log \left (5 \, x - 11\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.10, size = 29, normalized size = 0.83 \[ x\,\ln \left (\frac {5\,x-11}{76\,x+5}\right )-\frac {5\,\ln \left (x+\frac {5}{76}\right )}{76}-\frac {11\,\ln \left (x-\frac {11}{5}\right )}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.17, size = 32, normalized size = 0.91 \[ x \log {\left (\frac {5 x - 11}{76 x + 5} \right )} - \frac {11 \log {\left (x - \frac {11}{5} \right )}}{5} - \frac {5 \log {\left (x + \frac {5}{76} \right )}}{76} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________