Optimal. Leaf size=65 \[ -\frac{44}{2401 (3 x+2)}-\frac{11}{343 (3 x+2)^2}-\frac{11}{147 (3 x+2)^3}+\frac{1}{84 (3 x+2)^4}-\frac{88 \log (1-2 x)}{16807}+\frac{88 \log (3 x+2)}{16807} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0250805, 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} \[ -\frac{44}{2401 (3 x+2)}-\frac{11}{343 (3 x+2)^2}-\frac{11}{147 (3 x+2)^3}+\frac{1}{84 (3 x+2)^4}-\frac{88 \log (1-2 x)}{16807}+\frac{88 \log (3 x+2)}{16807} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin{align*} \int \frac{3+5 x}{(1-2 x) (2+3 x)^5} \, dx &=\int \left (-\frac{176}{16807 (-1+2 x)}-\frac{1}{7 (2+3 x)^5}+\frac{33}{49 (2+3 x)^4}+\frac{66}{343 (2+3 x)^3}+\frac{132}{2401 (2+3 x)^2}+\frac{264}{16807 (2+3 x)}\right ) \, dx\\ &=\frac{1}{84 (2+3 x)^4}-\frac{11}{147 (2+3 x)^3}-\frac{11}{343 (2+3 x)^2}-\frac{44}{2401 (2+3 x)}-\frac{88 \log (1-2 x)}{16807}+\frac{88 \log (2+3 x)}{16807}\\ \end{align*}
Mathematica [A] time = 0.0280386, size = 45, normalized size = 0.69 \[ \frac{-\frac{7 \left (4752 x^3+12276 x^2+12188 x+3963\right )}{(3 x+2)^4}-352 \log (3-6 x)+352 \log (3 x+2)}{67228} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.007, size = 54, normalized size = 0.8 \begin{align*} -{\frac{88\,\ln \left ( 2\,x-1 \right ) }{16807}}+{\frac{1}{84\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{11}{147\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{11}{343\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{44}{4802+7203\,x}}+{\frac{88\,\ln \left ( 2+3\,x \right ) }{16807}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 2.38907, size = 76, normalized size = 1.17 \begin{align*} -\frac{4752 \, x^{3} + 12276 \, x^{2} + 12188 \, x + 3963}{9604 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac{88}{16807} \, \log \left (3 \, x + 2\right ) - \frac{88}{16807} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.37018, size = 288, normalized size = 4.43 \begin{align*} -\frac{33264 \, x^{3} + 85932 \, x^{2} - 352 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 352 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (2 \, x - 1\right ) + 85316 \, x + 27741}{67228 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.165627, size = 54, normalized size = 0.83 \begin{align*} - \frac{4752 x^{3} + 12276 x^{2} + 12188 x + 3963}{777924 x^{4} + 2074464 x^{3} + 2074464 x^{2} + 921984 x + 153664} - \frac{88 \log{\left (x - \frac{1}{2} \right )}}{16807} + \frac{88 \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 = 3.02817, size = 70, normalized size = 1.08 \begin{align*} -\frac{44}{2401 \,{\left (3 \, x + 2\right )}} - \frac{11}{343 \,{\left (3 \, x + 2\right )}^{2}} - \frac{11}{147 \,{\left (3 \, x + 2\right )}^{3}} + \frac{1}{84 \,{\left (3 \, x + 2\right )}^{4}} - \frac{88}{16807} \, \log \left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]