Optimal. Leaf size=88 \[ -\frac {617100}{3 x+2}-\frac {166375}{5 x+3}-\frac {103455}{2 (3 x+2)^2}-\frac {5566}{(3 x+2)^3}-\frac {2541}{4 (3 x+2)^4}-\frac {3136}{45 (3 x+2)^5}-\frac {343}{54 (3 x+2)^6}+3584625 \log (3 x+2)-3584625 \log (5 x+3) \]
________________________________________________________________________________________
Rubi [A] time = 0.05, antiderivative size = 88, 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} \begin {gather*} -\frac {617100}{3 x+2}-\frac {166375}{5 x+3}-\frac {103455}{2 (3 x+2)^2}-\frac {5566}{(3 x+2)^3}-\frac {2541}{4 (3 x+2)^4}-\frac {3136}{45 (3 x+2)^5}-\frac {343}{54 (3 x+2)^6}+3584625 \log (3 x+2)-3584625 \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3}{(2+3 x)^7 (3+5 x)^2} \, dx &=\int \left (\frac {343}{3 (2+3 x)^7}+\frac {3136}{3 (2+3 x)^6}+\frac {7623}{(2+3 x)^5}+\frac {50094}{(2+3 x)^4}+\frac {310365}{(2+3 x)^3}+\frac {1851300}{(2+3 x)^2}+\frac {10753875}{2+3 x}+\frac {831875}{(3+5 x)^2}-\frac {17923125}{3+5 x}\right ) \, dx\\ &=-\frac {343}{54 (2+3 x)^6}-\frac {3136}{45 (2+3 x)^5}-\frac {2541}{4 (2+3 x)^4}-\frac {5566}{(2+3 x)^3}-\frac {103455}{2 (2+3 x)^2}-\frac {617100}{2+3 x}-\frac {166375}{3+5 x}+3584625 \log (2+3 x)-3584625 \log (3+5 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.12, size = 90, normalized size = 1.02 \begin {gather*} -\frac {617100}{3 x+2}-\frac {166375}{5 x+3}-\frac {103455}{2 (3 x+2)^2}-\frac {5566}{(3 x+2)^3}-\frac {2541}{4 (3 x+2)^4}-\frac {3136}{45 (3 x+2)^5}-\frac {343}{54 (3 x+2)^6}+3584625 \log (5 (3 x+2))-3584625 \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1-2 x)^3}{(2+3 x)^7 (3+5 x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.42, size = 155, normalized size = 1.76 \begin {gather*} -\frac {470374492500 \, x^{6} + 1865818820250 \, x^{5} + 3083217691950 \, x^{4} + 2716778541015 \, x^{3} + 1346292632205 \, x^{2} + 1935697500 \, {\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )} \log \left (5 \, x + 3\right ) - 1935697500 \, {\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )} \log \left (3 \, x + 2\right ) + 355739265638 \, x + 39157648662}{540 \, {\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.12, size = 85, normalized size = 0.97 \begin {gather*} -\frac {166375}{5 \, x + 3} + \frac {125 \, {\left (\frac {246075138}{5 \, x + 3} + \frac {181716633}{{\left (5 \, x + 3\right )}^{2}} + \frac {68296076}{{\left (5 \, x + 3\right )}^{3}} + \frac {13169954}{{\left (5 \, x + 3\right )}^{4}} + \frac {1059036}{{\left (5 \, x + 3\right )}^{5}} + 135033993\right )}}{4 \, {\left (\frac {1}{5 \, x + 3} + 3\right )}^{6}} + 3584625 \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 81, normalized size = 0.92 \begin {gather*} 3584625 \ln \left (3 x +2\right )-3584625 \ln \left (5 x +3\right )-\frac {343}{54 \left (3 x +2\right )^{6}}-\frac {3136}{45 \left (3 x +2\right )^{5}}-\frac {2541}{4 \left (3 x +2\right )^{4}}-\frac {5566}{\left (3 x +2\right )^{3}}-\frac {103455}{2 \left (3 x +2\right )^{2}}-\frac {617100}{3 x +2}-\frac {166375}{5 x +3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.48, size = 86, normalized size = 0.98 \begin {gather*} -\frac {470374492500 \, x^{6} + 1865818820250 \, x^{5} + 3083217691950 \, x^{4} + 2716778541015 \, x^{3} + 1346292632205 \, x^{2} + 355739265638 \, x + 39157648662}{540 \, {\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )}} - 3584625 \, \log \left (5 \, x + 3\right ) + 3584625 \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.15, size = 76, normalized size = 0.86 \begin {gather*} 7169250\,\mathrm {atanh}\left (30\,x+19\right )-\frac {238975\,x^6+\frac {5687605\,x^5}{6}+\frac {84587591\,x^4}{54}+\frac {248447969\,x^3}{180}+\frac {29917614049\,x^2}{43740}+\frac {177869632819\,x}{984150}+\frac {6526274777}{328050}}{x^7+\frac {23\,x^6}{5}+\frac {136\,x^5}{15}+\frac {268\,x^4}{27}+\frac {176\,x^3}{27}+\frac {208\,x^2}{81}+\frac {2048\,x}{3645}+\frac {64}{1215}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.22, size = 82, normalized size = 0.93 \begin {gather*} - \frac {470374492500 x^{6} + 1865818820250 x^{5} + 3083217691950 x^{4} + 2716778541015 x^{3} + 1346292632205 x^{2} + 355739265638 x + 39157648662}{1968300 x^{7} + 9054180 x^{6} + 17845920 x^{5} + 19537200 x^{4} + 12830400 x^{3} + 5054400 x^{2} + 1105920 x + 103680} - 3584625 \log {\left (x + \frac {3}{5} \right )} + 3584625 \log {\left (x + \frac {2}{3} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________