Optimal. Leaf size=65 \[ \frac{44}{2401 (1-2 x)}-\frac{128}{2401 (3 x+2)}-\frac{31}{686 (3 x+2)^2}+\frac{1}{147 (3 x+2)^3}-\frac{388 \log (1-2 x)}{16807}+\frac{388 \log (3 x+2)}{16807} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0306685, antiderivative size = 65, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ \frac{44}{2401 (1-2 x)}-\frac{128}{2401 (3 x+2)}-\frac{31}{686 (3 x+2)^2}+\frac{1}{147 (3 x+2)^3}-\frac{388 \log (1-2 x)}{16807}+\frac{388 \log (3 x+2)}{16807} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin{align*} \int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^4} \, dx &=\int \left (\frac{88}{2401 (-1+2 x)^2}-\frac{776}{16807 (-1+2 x)}-\frac{3}{49 (2+3 x)^4}+\frac{93}{343 (2+3 x)^3}+\frac{384}{2401 (2+3 x)^2}+\frac{1164}{16807 (2+3 x)}\right ) \, dx\\ &=\frac{44}{2401 (1-2 x)}+\frac{1}{147 (2+3 x)^3}-\frac{31}{686 (2+3 x)^2}-\frac{128}{2401 (2+3 x)}-\frac{388 \log (1-2 x)}{16807}+\frac{388 \log (2+3 x)}{16807}\\ \end{align*}
Mathematica [A] time = 0.0304381, size = 52, normalized size = 0.8 \[ \frac{-\frac{7 \left (20952 x^3+29682 x^2+6887 x-2164\right )}{(2 x-1) (3 x+2)^3}-2328 \log (3-6 x)+2328 \log (3 x+2)}{100842} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.007, size = 54, normalized size = 0.8 \begin{align*} -{\frac{44}{4802\,x-2401}}-{\frac{388\,\ln \left ( 2\,x-1 \right ) }{16807}}+{\frac{1}{147\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{31}{686\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{128}{4802+7203\,x}}+{\frac{388\,\ln \left ( 2+3\,x \right ) }{16807}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.10815, size = 76, normalized size = 1.17 \begin{align*} -\frac{20952 \, x^{3} + 29682 \, x^{2} + 6887 \, x - 2164}{14406 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} + \frac{388}{16807} \, \log \left (3 \, x + 2\right ) - \frac{388}{16807} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.13507, size = 282, normalized size = 4.34 \begin{align*} -\frac{146664 \, x^{3} + 207774 \, x^{2} - 2328 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (3 \, x + 2\right ) + 2328 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \log \left (2 \, x - 1\right ) + 48209 \, x - 15148}{100842 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.154955, size = 54, normalized size = 0.83 \begin{align*} - \frac{20952 x^{3} + 29682 x^{2} + 6887 x - 2164}{777924 x^{4} + 1166886 x^{3} + 259308 x^{2} - 288120 x - 115248} - \frac{388 \log{\left (x - \frac{1}{2} \right )}}{16807} + \frac{388 \log{\left (x + \frac{2}{3} \right )}}{16807} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.87681, size = 81, normalized size = 1.25 \begin{align*} -\frac{44}{2401 \,{\left (2 \, x - 1\right )}} + \frac{18 \,{\left (\frac{2415}{2 \, x - 1} + \frac{3038}{{\left (2 \, x - 1\right )}^{2}} + 473\right )}}{16807 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{3}} + \frac{388}{16807} \, \log \left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]