Optimal. Leaf size=76 \[ \frac {388}{16807 (1-2 x)}-\frac {558}{16807 (3 x+2)}+\frac {22}{2401 (1-2 x)^2}-\frac {87}{4802 (3 x+2)^2}+\frac {1}{343 (3 x+2)^3}-\frac {2280 \log (1-2 x)}{117649}+\frac {2280 \log (3 x+2)}{117649} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 76, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ \frac {388}{16807 (1-2 x)}-\frac {558}{16807 (3 x+2)}+\frac {22}{2401 (1-2 x)^2}-\frac {87}{4802 (3 x+2)^2}+\frac {1}{343 (3 x+2)^3}-\frac {2280 \log (1-2 x)}{117649}+\frac {2280 \log (3 x+2)}{117649} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int \frac {3+5 x}{(1-2 x)^3 (2+3 x)^4} \, dx &=\int \left (-\frac {88}{2401 (-1+2 x)^3}+\frac {776}{16807 (-1+2 x)^2}-\frac {4560}{117649 (-1+2 x)}-\frac {9}{343 (2+3 x)^4}+\frac {261}{2401 (2+3 x)^3}+\frac {1674}{16807 (2+3 x)^2}+\frac {6840}{117649 (2+3 x)}\right ) \, dx\\ &=\frac {22}{2401 (1-2 x)^2}+\frac {388}{16807 (1-2 x)}+\frac {1}{343 (2+3 x)^3}-\frac {87}{4802 (2+3 x)^2}-\frac {558}{16807 (2+3 x)}-\frac {2280 \log (1-2 x)}{117649}+\frac {2280 \log (2+3 x)}{117649}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.05, size = 57, normalized size = 0.75 \[ \frac {-\frac {7 \left (82080 x^4+75240 x^3-31160 x^2-33725 x-3088\right )}{(1-2 x)^2 (3 x+2)^3}-4560 \log (3-6 x)+4560 \log (3 x+2)}{235298} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.72, size = 115, normalized size = 1.51 \[ -\frac {574560 \, x^{4} + 526680 \, x^{3} - 218120 \, x^{2} - 4560 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 4560 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )} \log \left (2 \, x - 1\right ) - 236075 \, x - 21616}{235298 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.28, size = 55, normalized size = 0.72 \[ -\frac {82080 \, x^{4} + 75240 \, x^{3} - 31160 \, x^{2} - 33725 \, x - 3088}{33614 \, {\left (3 \, x + 2\right )}^{3} {\left (2 \, x - 1\right )}^{2}} + \frac {2280}{117649} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {2280}{117649} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 63, normalized size = 0.83 \[ -\frac {2280 \ln \left (2 x -1\right )}{117649}+\frac {2280 \ln \left (3 x +2\right )}{117649}+\frac {1}{343 \left (3 x +2\right )^{3}}-\frac {87}{4802 \left (3 x +2\right )^{2}}-\frac {558}{16807 \left (3 x +2\right )}+\frac {22}{2401 \left (2 x -1\right )^{2}}-\frac {388}{16807 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.52, size = 66, normalized size = 0.87 \[ -\frac {82080 \, x^{4} + 75240 \, x^{3} - 31160 \, x^{2} - 33725 \, x - 3088}{33614 \, {\left (108 \, x^{5} + 108 \, x^{4} - 45 \, x^{3} - 58 \, x^{2} + 4 \, x + 8\right )}} + \frac {2280}{117649} \, \log \left (3 \, x + 2\right ) - \frac {2280}{117649} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 53, normalized size = 0.70 \[ \frac {4560\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{117649}+\frac {-\frac {380\,x^4}{16807}-\frac {1045\,x^3}{50421}+\frac {3895\,x^2}{453789}+\frac {33725\,x}{3630312}+\frac {386}{453789}}{x^5+x^4-\frac {5\,x^3}{12}-\frac {29\,x^2}{54}+\frac {x}{27}+\frac {2}{27}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.19, size = 65, normalized size = 0.86 \[ - \frac {82080 x^{4} + 75240 x^{3} - 31160 x^{2} - 33725 x - 3088}{3630312 x^{5} + 3630312 x^{4} - 1512630 x^{3} - 1949612 x^{2} + 134456 x + 268912} - \frac {2280 \log {\left (x - \frac {1}{2} \right )}}{117649} + \frac {2280 \log {\left (x + \frac {2}{3} \right )}}{117649} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________