Optimal. Leaf size=33 \[ \frac{9}{2} \log (a-x)-17 \log (2 a-x)+\frac{35}{2} \log (3 a-x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0538914, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 39, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.026, Rules used = {2074} \[ \frac{9}{2} \log (a-x)-17 \log (2 a-x)+\frac{35}{2} \log (3 a-x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2074
Rubi steps
\begin{align*} \int \frac{11 a^2-7 a x+5 x^2}{-6 a^3+11 a^2 x-6 a x^2+x^3} \, dx &=\int \left (-\frac{9}{2 (a-x)}+\frac{17}{2 a-x}-\frac{35}{2 (3 a-x)}\right ) \, dx\\ &=\frac{9}{2} \log (a-x)-17 \log (2 a-x)+\frac{35}{2} \log (3 a-x)\\ \end{align*}
Mathematica [A] time = 0.014098, size = 29, normalized size = 0.88 \[ \frac{35}{2} \log (x-3 a)-17 \log (x-2 a)+\frac{9}{2} \log (x-a) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.008, size = 26, normalized size = 0.8 \begin{align*}{\frac{35\,\ln \left ( x-3\,a \right ) }{2}}+{\frac{9\,\ln \left ( -a+x \right ) }{2}}-17\,\ln \left ( x-2\,a \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.938507, size = 34, normalized size = 1.03 \begin{align*} \frac{9}{2} \, \log \left (-a + x\right ) - 17 \, \log \left (-2 \, a + x\right ) + \frac{35}{2} \, \log \left (-3 \, a + x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.82003, size = 77, normalized size = 2.33 \begin{align*} \frac{9}{2} \, \log \left (-a + x\right ) - 17 \, \log \left (-2 \, a + x\right ) + \frac{35}{2} \, \log \left (-3 \, a + x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.371312, size = 26, normalized size = 0.79 \begin{align*} \frac{35 \log{\left (- 3 a + x \right )}}{2} - 17 \log{\left (- 2 a + x \right )} + \frac{9 \log{\left (- a + x \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.05728, size = 38, normalized size = 1.15 \begin{align*} \frac{9}{2} \, \log \left ({\left | -a + x \right |}\right ) - 17 \, \log \left ({\left | -2 \, a + x \right |}\right ) + \frac{35}{2} \, \log \left ({\left | -3 \, a + x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]