Optimal. Leaf size=97 \[ \frac {6528}{35153041 (1-2 x)}+\frac {26973}{2401 (3 x+2)}+\frac {290625}{14641 (5 x+3)}+\frac {16}{456533 (1-2 x)^2}+\frac {243}{686 (3 x+2)^2}-\frac {3125}{2662 (5 x+3)^2}-\frac {776928 \log (1-2 x)}{2706784157}-\frac {1944972 \log (3 x+2)}{16807}+\frac {18637500 \log (5 x+3)}{161051} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.05, antiderivative size = 97, 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} \[ \frac {6528}{35153041 (1-2 x)}+\frac {26973}{2401 (3 x+2)}+\frac {290625}{14641 (5 x+3)}+\frac {16}{456533 (1-2 x)^2}+\frac {243}{686 (3 x+2)^2}-\frac {3125}{2662 (5 x+3)^2}-\frac {776928 \log (1-2 x)}{2706784157}-\frac {1944972 \log (3 x+2)}{16807}+\frac {18637500 \log (5 x+3)}{161051} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^3 (2+3 x)^3 (3+5 x)^3} \, dx &=\int \left (-\frac {64}{456533 (-1+2 x)^3}+\frac {13056}{35153041 (-1+2 x)^2}-\frac {1553856}{2706784157 (-1+2 x)}-\frac {729}{343 (2+3 x)^3}-\frac {80919}{2401 (2+3 x)^2}-\frac {5834916}{16807 (2+3 x)}+\frac {15625}{1331 (3+5 x)^3}-\frac {1453125}{14641 (3+5 x)^2}+\frac {93187500}{161051 (3+5 x)}\right ) \, dx\\ &=\frac {16}{456533 (1-2 x)^2}+\frac {6528}{35153041 (1-2 x)}+\frac {243}{686 (2+3 x)^2}+\frac {26973}{2401 (2+3 x)}-\frac {3125}{2662 (3+5 x)^2}+\frac {290625}{14641 (3+5 x)}-\frac {776928 \log (1-2 x)}{2706784157}-\frac {1944972 \log (2+3 x)}{16807}+\frac {18637500 \log (3+5 x)}{161051}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.21, size = 88, normalized size = 0.91 \[ \frac {2 \left (\frac {77}{4} \left (\frac {789823386}{3 x+2}+\frac {1395581250}{5 x+3}+\frac {24904341}{(3 x+2)^2}-\frac {82534375}{(5 x+3)^2}+\frac {13056}{1-2 x}+\frac {2464}{(1-2 x)^2}\right )-388464 \log (1-2 x)-156619842786 \log (6 x+4)+156620231250 \log (10 x+6)\right )}{2706784157} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.61, size = 173, normalized size = 1.78 \[ \frac {37587223951200 \, x^{5} + 33827604204240 \, x^{4} - 16859483294808 \, x^{3} - 17801732753112 \, x^{2} + 626480925000 \, {\left (900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right )} \log \left (5 \, x + 3\right ) - 626479371144 \, {\left (900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right )} \log \left (3 \, x + 2\right ) - 1553856 \, {\left (900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right )} \log \left (2 \, x - 1\right ) + 1786038929444 \, x + 2376093430249}{5413568314 \, {\left (900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.22, size = 72, normalized size = 0.74 \[ \frac {488145765600 \, x^{5} + 439319535120 \, x^{4} - 218954328504 \, x^{3} - 231191334456 \, x^{2} + 23195310772 \, x + 30858356237}{70306082 \, {\left (30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right )}^{2}} + \frac {18637500}{161051} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {1944972}{16807} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {776928}{2706784157} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 80, normalized size = 0.82 \[ -\frac {776928 \ln \left (2 x -1\right )}{2706784157}-\frac {1944972 \ln \left (3 x +2\right )}{16807}+\frac {18637500 \ln \left (5 x +3\right )}{161051}-\frac {3125}{2662 \left (5 x +3\right )^{2}}+\frac {290625}{14641 \left (5 x +3\right )}+\frac {243}{686 \left (3 x +2\right )^{2}}+\frac {26973}{2401 \left (3 x +2\right )}+\frac {16}{456533 \left (2 x -1\right )^{2}}-\frac {6528}{35153041 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.50, size = 84, normalized size = 0.87 \[ \frac {488145765600 \, x^{5} + 439319535120 \, x^{4} - 218954328504 \, x^{3} - 231191334456 \, x^{2} + 23195310772 \, x + 30858356237}{70306082 \, {\left (900 \, x^{6} + 1380 \, x^{5} + 109 \, x^{4} - 682 \, x^{3} - 227 \, x^{2} + 84 \, x + 36\right )}} + \frac {18637500}{161051} \, \log \left (5 \, x + 3\right ) - \frac {1944972}{16807} \, \log \left (3 \, x + 2\right ) - \frac {776928}{2706784157} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.07, size = 75, normalized size = 0.77 \[ \frac {18637500\,\ln \left (x+\frac {3}{5}\right )}{161051}-\frac {1944972\,\ln \left (x+\frac {2}{3}\right )}{16807}-\frac {776928\,\ln \left (x-\frac {1}{2}\right )}{2706784157}+\frac {\frac {271192092\,x^5}{35153041}+\frac {1220332042\,x^4}{175765205}-\frac {9123097021\,x^3}{2636478075}-\frac {9632972269\,x^2}{2636478075}+\frac {5798827693\,x}{15818868450}+\frac {30858356237}{63275473800}}{x^6+\frac {23\,x^5}{15}+\frac {109\,x^4}{900}-\frac {341\,x^3}{450}-\frac {227\,x^2}{900}+\frac {7\,x}{75}+\frac {1}{25}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.28, size = 85, normalized size = 0.88 \[ - \frac {- 488145765600 x^{5} - 439319535120 x^{4} + 218954328504 x^{3} + 231191334456 x^{2} - 23195310772 x - 30858356237}{63275473800 x^{6} + 97022393160 x^{5} + 7663362938 x^{4} - 47948747924 x^{3} - 15959480614 x^{2} + 5905710888 x + 2531018952} - \frac {776928 \log {\left (x - \frac {1}{2} \right )}}{2706784157} + \frac {18637500 \log {\left (x + \frac {3}{5} \right )}}{161051} - \frac {1944972 \log {\left (x + \frac {2}{3} \right )}}{16807} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________