Optimal. Leaf size=54 \[ \frac{22}{343 (1-2 x)}-\frac{31}{343 (3 x+2)}+\frac{1}{98 (3 x+2)^2}-\frac{128 \log (1-2 x)}{2401}+\frac{128 \log (3 x+2)}{2401} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0239423, antiderivative size = 54, 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} \[ \frac{22}{343 (1-2 x)}-\frac{31}{343 (3 x+2)}+\frac{1}{98 (3 x+2)^2}-\frac{128 \log (1-2 x)}{2401}+\frac{128 \log (3 x+2)}{2401} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin{align*} \int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^3} \, dx &=\int \left (\frac{44}{343 (-1+2 x)^2}-\frac{256}{2401 (-1+2 x)}-\frac{3}{49 (2+3 x)^3}+\frac{93}{343 (2+3 x)^2}+\frac{384}{2401 (2+3 x)}\right ) \, dx\\ &=\frac{22}{343 (1-2 x)}+\frac{1}{98 (2+3 x)^2}-\frac{31}{343 (2+3 x)}-\frac{128 \log (1-2 x)}{2401}+\frac{128 \log (2+3 x)}{2401}\\ \end{align*}
Mathematica [A] time = 0.0273639, size = 47, normalized size = 0.87 \[ \frac{-\frac{7 \left (768 x^2+576 x+59\right )}{(2 x-1) (3 x+2)^2}-256 \log (1-2 x)+256 \log (6 x+4)}{4802} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.008, size = 45, normalized size = 0.8 \begin{align*} -{\frac{22}{686\,x-343}}-{\frac{128\,\ln \left ( 2\,x-1 \right ) }{2401}}+{\frac{1}{98\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{31}{686+1029\,x}}+{\frac{128\,\ln \left ( 2+3\,x \right ) }{2401}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 2.29799, size = 62, normalized size = 1.15 \begin{align*} -\frac{768 \, x^{2} + 576 \, x + 59}{686 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} + \frac{128}{2401} \, \log \left (3 \, x + 2\right ) - \frac{128}{2401} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.4317, size = 212, normalized size = 3.93 \begin{align*} -\frac{5376 \, x^{2} - 256 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (3 \, x + 2\right ) + 256 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )} \log \left (2 \, x - 1\right ) + 4032 \, x + 413}{4802 \,{\left (18 \, x^{3} + 15 \, x^{2} - 4 \, x - 4\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.143687, size = 44, normalized size = 0.81 \begin{align*} - \frac{768 x^{2} + 576 x + 59}{12348 x^{3} + 10290 x^{2} - 2744 x - 2744} - \frac{128 \log{\left (x - \frac{1}{2} \right )}}{2401} + \frac{128 \log{\left (x + \frac{2}{3} \right )}}{2401} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.74246, size = 69, normalized size = 1.28 \begin{align*} -\frac{22}{343 \,{\left (2 \, x - 1\right )}} + \frac{6 \,{\left (\frac{203}{2 \, x - 1} + 90\right )}}{2401 \,{\left (\frac{7}{2 \, x - 1} + 3\right )}^{2}} + \frac{128}{2401} \, \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]