Optimal. Leaf size=65 \[ -\frac {242}{2401 (3 x+2)}-\frac {121}{686 (3 x+2)^2}+\frac {68}{1323 (3 x+2)^3}-\frac {1}{252 (3 x+2)^4}-\frac {484 \log (1-2 x)}{16807}+\frac {484 \log (3 x+2)}{16807} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 65, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \[ -\frac {242}{2401 (3 x+2)}-\frac {121}{686 (3 x+2)^2}+\frac {68}{1323 (3 x+2)^3}-\frac {1}{252 (3 x+2)^4}-\frac {484 \log (1-2 x)}{16807}+\frac {484 \log (3 x+2)}{16807} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin {align*} \int \frac {(3+5 x)^2}{(1-2 x) (2+3 x)^5} \, dx &=\int \left (-\frac {968}{16807 (-1+2 x)}+\frac {1}{21 (2+3 x)^5}-\frac {68}{147 (2+3 x)^4}+\frac {363}{343 (2+3 x)^3}+\frac {726}{2401 (2+3 x)^2}+\frac {1452}{16807 (2+3 x)}\right ) \, dx\\ &=-\frac {1}{252 (2+3 x)^4}+\frac {68}{1323 (2+3 x)^3}-\frac {121}{686 (2+3 x)^2}-\frac {242}{2401 (2+3 x)}-\frac {484 \log (1-2 x)}{16807}+\frac {484 \log (2+3 x)}{16807}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.05, size = 47, normalized size = 0.72 \[ \frac {2 \left (-\frac {7 \left (705672 x^3+1822986 x^2+1449768 x+366413\right )}{8 (3 x+2)^4}-6534 \log (1-2 x)+6534 \log (6 x+4)\right )}{453789} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.76, size = 95, normalized size = 1.46 \[ -\frac {4939704 \, x^{3} + 12760902 \, x^{2} - 52272 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 52272 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (2 \, x - 1\right ) + 10148376 \, x + 2564891}{1815156 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.95, size = 52, normalized size = 0.80 \[ -\frac {242}{2401 \, {\left (3 \, x + 2\right )}} - \frac {121}{686 \, {\left (3 \, x + 2\right )}^{2}} + \frac {68}{1323 \, {\left (3 \, x + 2\right )}^{3}} - \frac {1}{252 \, {\left (3 \, x + 2\right )}^{4}} - \frac {484}{16807} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 54, normalized size = 0.83 \[ -\frac {484 \ln \left (2 x -1\right )}{16807}+\frac {484 \ln \left (3 x +2\right )}{16807}-\frac {1}{252 \left (3 x +2\right )^{4}}+\frac {68}{1323 \left (3 x +2\right )^{3}}-\frac {121}{686 \left (3 x +2\right )^{2}}-\frac {242}{2401 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.50, size = 56, normalized size = 0.86 \[ -\frac {705672 \, x^{3} + 1822986 \, x^{2} + 1449768 \, x + 366413}{259308 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac {484}{16807} \, \log \left (3 \, x + 2\right ) - \frac {484}{16807} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.13, size = 46, normalized size = 0.71 \[ \frac {968\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{16807}-\frac {\frac {242\,x^3}{7203}+\frac {3751\,x^2}{43218}+\frac {120814\,x}{1750329}+\frac {366413}{21003948}}{x^4+\frac {8\,x^3}{3}+\frac {8\,x^2}{3}+\frac {32\,x}{27}+\frac {16}{81}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.18, size = 54, normalized size = 0.83 \[ - \frac {705672 x^{3} + 1822986 x^{2} + 1449768 x + 366413}{21003948 x^{4} + 56010528 x^{3} + 56010528 x^{2} + 24893568 x + 4148928} - \frac {484 \log {\left (x - \frac {1}{2} \right )}}{16807} + \frac {484 \log {\left (x + \frac {2}{3} \right )}}{16807} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________