Optimal. Leaf size=70 \[ \frac {117649}{42592 (1-2 x)^2}-\frac {1563051}{234256 (1-2 x)}-\frac {729 x}{1000}-\frac {1}{1663750 (3+5 x)^2}-\frac {204}{9150625 (3+5 x)}-\frac {6950895 \log (1-2 x)}{2576816}+\frac {17547 \log (3+5 x)}{100656875} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 70, 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 = {90}
\begin {gather*} -\frac {729 x}{1000}-\frac {1563051}{234256 (1-2 x)}-\frac {204}{9150625 (5 x+3)}+\frac {117649}{42592 (1-2 x)^2}-\frac {1}{1663750 (5 x+3)^2}-\frac {6950895 \log (1-2 x)}{2576816}+\frac {17547 \log (5 x+3)}{100656875} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^6}{(1-2 x)^3 (3+5 x)^3} \, dx &=\int \left (-\frac {729}{1000}-\frac {117649}{10648 (-1+2 x)^3}-\frac {1563051}{117128 (-1+2 x)^2}-\frac {6950895}{1288408 (-1+2 x)}+\frac {1}{166375 (3+5 x)^3}+\frac {204}{1830125 (3+5 x)^2}+\frac {17547}{20131375 (3+5 x)}\right ) \, dx\\ &=\frac {117649}{42592 (1-2 x)^2}-\frac {1563051}{234256 (1-2 x)}-\frac {729 x}{1000}-\frac {1}{1663750 (3+5 x)^2}-\frac {204}{9150625 (3+5 x)}-\frac {6950895 \log (1-2 x)}{2576816}+\frac {17547 \log (3+5 x)}{100656875}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.03, size = 60, normalized size = 0.86 \begin {gather*} \frac {-\frac {55 \left (2317121263+49588250 x-19656314001 x^2-21487765512 x^3+3700073520 x^4+4269315600 x^5\right )}{\left (-3+x+10 x^2\right )^2}-8688618750 \log (3-6 x)+561504 \log (-3 (3+5 x))}{3221020000} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.11, size = 57, normalized size = 0.81
method | result | size |
risch | \(-\frac {729 x}{1000}+\frac {\frac {4884527847}{14641000} x^{3}+\frac {17720890929}{58564000} x^{2}+\frac {16387753}{5856400} x -\frac {2060962327}{58564000}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {6950895 \ln \left (-1+2 x \right )}{2576816}+\frac {17547 \ln \left (3+5 x \right )}{100656875}\) | \(52\) |
norman | \(\frac {-\frac {678981653}{8784600} x^{4}+\frac {15991853509}{43923000} x^{3}+\frac {30215897689}{87846000} x^{2}-\frac {729}{10} x^{5}-\frac {1195751819}{29282000}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {6950895 \ln \left (-1+2 x \right )}{2576816}+\frac {17547 \ln \left (3+5 x \right )}{100656875}\) | \(55\) |
default | \(-\frac {729 x}{1000}+\frac {117649}{42592 \left (-1+2 x \right )^{2}}+\frac {1563051}{234256 \left (-1+2 x \right )}-\frac {6950895 \ln \left (-1+2 x \right )}{2576816}-\frac {1}{1663750 \left (3+5 x \right )^{2}}-\frac {204}{9150625 \left (3+5 x \right )}+\frac {17547 \ln \left (3+5 x \right )}{100656875}\) | \(57\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.33, size = 59, normalized size = 0.84 \begin {gather*} -\frac {729}{1000} \, x + \frac {19538111388 \, x^{3} + 17720890929 \, x^{2} + 163877530 \, x - 2060962327}{58564000 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac {17547}{100656875} \, \log \left (5 \, x + 3\right ) - \frac {6950895}{2576816} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.72, size = 105, normalized size = 1.50 \begin {gather*} -\frac {234812358000 \, x^{5} + 46962471600 \, x^{4} - 1213135417560 \, x^{3} - 988737742575 \, x^{2} - 561504 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 8688618750 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 12119848070 \, x + 113352927985}{3221020000 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.09, size = 60, normalized size = 0.86 \begin {gather*} - \frac {729 x}{1000} - \frac {- 19538111388 x^{3} - 17720890929 x^{2} - 163877530 x + 2060962327}{5856400000 x^{4} + 1171280000 x^{3} - 3455276000 x^{2} - 351384000 x + 527076000} - \frac {6950895 \log {\left (x - \frac {1}{2} \right )}}{2576816} + \frac {17547 \log {\left (x + \frac {3}{5} \right )}}{100656875} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.58, size = 53, normalized size = 0.76 \begin {gather*} -\frac {729}{1000} \, x + \frac {19538111388 \, x^{3} + 17720890929 \, x^{2} + 163877530 \, x - 2060962327}{58564000 \, {\left (5 \, x + 3\right )}^{2} {\left (2 \, x - 1\right )}^{2}} + \frac {17547}{100656875} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {6950895}{2576816} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.09, size = 52, normalized size = 0.74 \begin {gather*} \frac {17547\,\ln \left (x+\frac {3}{5}\right )}{100656875}-\frac {6950895\,\ln \left (x-\frac {1}{2}\right )}{2576816}-\frac {729\,x}{1000}+\frac {\frac {4884527847\,x^3}{1464100000}+\frac {17720890929\,x^2}{5856400000}+\frac {16387753\,x}{585640000}-\frac {2060962327}{5856400000}}{x^4+\frac {x^3}{5}-\frac {59\,x^2}{100}-\frac {3\,x}{50}+\frac {9}{100}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________