Optimal. Leaf size=86 \[ \frac {32}{184877 (1-2 x)}+\frac {434043}{16807 (3 x+2)}+\frac {12393}{4802 (3 x+2)^2}+\frac {117}{343 (3 x+2)^3}+\frac {9}{196 (3 x+2)^4}-\frac {6400 \log (1-2 x)}{14235529}-\frac {15192225 \log (3 x+2)}{117649}+\frac {15625}{121} \log (5 x+3) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.05, antiderivative size = 86, 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} \[ \frac {32}{184877 (1-2 x)}+\frac {434043}{16807 (3 x+2)}+\frac {12393}{4802 (3 x+2)^2}+\frac {117}{343 (3 x+2)^3}+\frac {9}{196 (3 x+2)^4}-\frac {6400 \log (1-2 x)}{14235529}-\frac {15192225 \log (3 x+2)}{117649}+\frac {15625}{121} \log (5 x+3) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^2 (2+3 x)^5 (3+5 x)} \, dx &=\int \left (\frac {64}{184877 (-1+2 x)^2}-\frac {12800}{14235529 (-1+2 x)}-\frac {27}{49 (2+3 x)^5}-\frac {1053}{343 (2+3 x)^4}-\frac {37179}{2401 (2+3 x)^3}-\frac {1302129}{16807 (2+3 x)^2}-\frac {45576675}{117649 (2+3 x)}+\frac {78125}{121 (3+5 x)}\right ) \, dx\\ &=\frac {32}{184877 (1-2 x)}+\frac {9}{196 (2+3 x)^4}+\frac {117}{343 (2+3 x)^3}+\frac {12393}{4802 (2+3 x)^2}+\frac {434043}{16807 (2+3 x)}-\frac {6400 \log (1-2 x)}{14235529}-\frac {15192225 \log (2+3 x)}{117649}+\frac {15625}{121} \log (3+5 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.12, size = 81, normalized size = 0.94 \[ \frac {5 \left (\frac {77}{5} \left (\frac {19097892}{3 x+2}+\frac {1908522}{(3 x+2)^2}+\frac {252252}{(3 x+2)^3}+\frac {33957}{(3 x+2)^4}+\frac {128}{1-2 x}\right )-5120 \log (5-10 x)-1470607380 \log (5 (3 x+2))+1470612500 \log (5 x+3)\right )}{56942116} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.94, size = 148, normalized size = 1.72 \[ \frac {79408236600 \, x^{4} + 121756635000 \, x^{3} + 28788432750 \, x^{2} + 7353062500 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )} \log \left (5 \, x + 3\right ) - 7353036900 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )} \log \left (3 \, x + 2\right ) - 25600 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )} \log \left (2 \, x - 1\right ) - 29974871850 \, x - 12393745441}{56942116 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.19, size = 82, normalized size = 0.95 \[ \frac {434043}{16807 \, {\left (3 \, x + 2\right )}} + \frac {192}{1294139 \, {\left (\frac {7}{3 \, x + 2} - 2\right )}} + \frac {12393}{4802 \, {\left (3 \, x + 2\right )}^{2}} + \frac {117}{343 \, {\left (3 \, x + 2\right )}^{3}} + \frac {9}{196 \, {\left (3 \, x + 2\right )}^{4}} + \frac {15625}{121} \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) - \frac {6400}{14235529} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 71, normalized size = 0.83 \[ -\frac {6400 \ln \left (2 x -1\right )}{14235529}-\frac {15192225 \ln \left (3 x +2\right )}{117649}+\frac {15625 \ln \left (5 x +3\right )}{121}+\frac {9}{196 \left (3 x +2\right )^{4}}+\frac {117}{343 \left (3 x +2\right )^{3}}+\frac {12393}{4802 \left (3 x +2\right )^{2}}+\frac {434043}{16807 \left (3 x +2\right )}-\frac {32}{184877 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.57, size = 74, normalized size = 0.86 \[ \frac {1031275800 \, x^{4} + 1581255000 \, x^{3} + 373875750 \, x^{2} - 389284050 \, x - 160957733}{739508 \, {\left (162 \, x^{5} + 351 \, x^{4} + 216 \, x^{3} - 24 \, x^{2} - 64 \, x - 16\right )}} + \frac {15625}{121} \, \log \left (5 \, x + 3\right ) - \frac {15192225}{117649} \, \log \left (3 \, x + 2\right ) - \frac {6400}{14235529} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.09, size = 68, normalized size = 0.79 \[ \frac {15625\,\ln \left (x+\frac {3}{5}\right )}{121}-\frac {15192225\,\ln \left (x+\frac {2}{3}\right )}{117649}-\frac {6400\,\ln \left (x-\frac {1}{2}\right )}{14235529}-\frac {\frac {1591475\,x^4}{184877}+\frac {7320625\,x^3}{554631}+\frac {2307875\,x^2}{739508}-\frac {64880675\,x}{19966716}-\frac {160957733}{119800296}}{-x^5-\frac {13\,x^4}{6}-\frac {4\,x^3}{3}+\frac {4\,x^2}{27}+\frac {32\,x}{81}+\frac {8}{81}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.26, size = 75, normalized size = 0.87 \[ \frac {1031275800 x^{4} + 1581255000 x^{3} + 373875750 x^{2} - 389284050 x - 160957733}{119800296 x^{5} + 259567308 x^{4} + 159733728 x^{3} - 17748192 x^{2} - 47328512 x - 11832128} - \frac {6400 \log {\left (x - \frac {1}{2} \right )}}{14235529} + \frac {15625 \log {\left (x + \frac {3}{5} \right )}}{121} - \frac {15192225 \log {\left (x + \frac {2}{3} \right )}}{117649} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________