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 = 0.0058722, antiderivative size = 35, normalized size of antiderivative = 1., 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 2486
Rule 31
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 = 0.0049719, 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]
________________________________________________________________________________________
Maple [A] time = 0.01, size = 44, normalized size = 1.3 \begin{align*}{\frac{861}{380}\ln \left ( -861\, \left ( 5+76\,x \right ) ^{-1} \right ) }+{\frac{5+76\,x}{5}\ln \left ({\frac{5}{76}}-{\frac{861}{380+5776\,x}} \right ) \left ({\frac{5}{76}}-{\frac{861}{380+5776\,x}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.00665, size = 45, normalized size = 1.29 \begin{align*} 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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.77686, size = 97, normalized size = 2.77 \begin{align*} 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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.160948, size = 32, normalized size = 0.91 \begin{align*} 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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.19923, size = 47, normalized size = 1.34 \begin{align*} x \log \left (\frac{5 \, x - 11}{76 \, x + 5}\right ) - \frac{5}{76} \, \log \left ({\left | 76 \, x + 5 \right |}\right ) - \frac{11}{5} \, \log \left ({\left | 5 \, x - 11 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]