Optimal. Leaf size=65 \[ -\frac {2187 x^5}{250}-\frac {86751 x^4}{2000}-\frac {495477 x^3}{5000}-\frac {14750667 x^2}{100000}-\frac {19846971 x}{100000}-\frac {1}{859375 (5 x+3)}-\frac {823543 \log (1-2 x)}{7744}+\frac {233 \log (5 x+3)}{9453125} \]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 65, 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 {2187 x^5}{250}-\frac {86751 x^4}{2000}-\frac {495477 x^3}{5000}-\frac {14750667 x^2}{100000}-\frac {19846971 x}{100000}-\frac {1}{859375 (5 x+3)}-\frac {823543 \log (1-2 x)}{7744}+\frac {233 \log (5 x+3)}{9453125} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^7}{(1-2 x) (3+5 x)^2} \, dx &=\int \left (-\frac {19846971}{100000}-\frac {14750667 x}{50000}-\frac {1486431 x^2}{5000}-\frac {86751 x^3}{500}-\frac {2187 x^4}{50}-\frac {823543}{3872 (-1+2 x)}+\frac {1}{171875 (3+5 x)^2}+\frac {233}{1890625 (3+5 x)}\right ) \, dx\\ &=-\frac {19846971 x}{100000}-\frac {14750667 x^2}{100000}-\frac {495477 x^3}{5000}-\frac {86751 x^4}{2000}-\frac {2187 x^5}{250}-\frac {1}{859375 (3+5 x)}-\frac {823543 \log (1-2 x)}{7744}+\frac {233 \log (3+5 x)}{9453125}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.04, size = 60, normalized size = 0.92 \begin {gather*} \frac {-\frac {11 \left (9622800000 x^6+53486730000 x^5+137632770000 x^4+227660301000 x^3+315671083200 x^2-35641061775 x-99978641969\right )}{5 x+3}-257357187500 \log (1-2 x)+59648 \log (10 x+6)}{2420000000} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(2+3 x)^7}{(1-2 x) (3+5 x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.37, size = 65, normalized size = 1.00 \begin {gather*} -\frac {26462700000 \, x^{6} + 147088507500 \, x^{5} + 378490117500 \, x^{4} + 626065827750 \, x^{3} + 868095478800 \, x^{2} - 14912 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 64339296875 \, {\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 360222523650 \, x + 704}{605000000 \, {\left (5 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.01, size = 90, normalized size = 1.38 \begin {gather*} -\frac {27}{12500000} \, {\left (5 \, x + 3\right )}^{5} {\left (\frac {12690}{5 \, x + 3} + \frac {98100}{{\left (5 \, x + 3\right )}^{2}} + \frac {813525}{{\left (5 \, x + 3\right )}^{3}} + \frac {8951575}{{\left (5 \, x + 3\right )}^{4}} + 1296\right )} - \frac {1}{859375 \, {\left (5 \, x + 3\right )}} + \frac {531729603}{5000000} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) - \frac {823543}{7744} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 50, normalized size = 0.77 \begin {gather*} -\frac {2187 x^{5}}{250}-\frac {86751 x^{4}}{2000}-\frac {495477 x^{3}}{5000}-\frac {14750667 x^{2}}{100000}-\frac {19846971 x}{100000}-\frac {823543 \ln \left (2 x -1\right )}{7744}+\frac {233 \ln \left (5 x +3\right )}{9453125}-\frac {1}{859375 \left (5 x +3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.57, size = 49, normalized size = 0.75 \begin {gather*} -\frac {2187}{250} \, x^{5} - \frac {86751}{2000} \, x^{4} - \frac {495477}{5000} \, x^{3} - \frac {14750667}{100000} \, x^{2} - \frac {19846971}{100000} \, x - \frac {1}{859375 \, {\left (5 \, x + 3\right )}} + \frac {233}{9453125} \, \log \left (5 \, x + 3\right ) - \frac {823543}{7744} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 45, normalized size = 0.69 \begin {gather*} \frac {233\,\ln \left (x+\frac {3}{5}\right )}{9453125}-\frac {823543\,\ln \left (x-\frac {1}{2}\right )}{7744}-\frac {19846971\,x}{100000}-\frac {1}{4296875\,\left (x+\frac {3}{5}\right )}-\frac {14750667\,x^2}{100000}-\frac {495477\,x^3}{5000}-\frac {86751\,x^4}{2000}-\frac {2187\,x^5}{250} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.17, size = 58, normalized size = 0.89 \begin {gather*} - \frac {2187 x^{5}}{250} - \frac {86751 x^{4}}{2000} - \frac {495477 x^{3}}{5000} - \frac {14750667 x^{2}}{100000} - \frac {19846971 x}{100000} - \frac {823543 \log {\left (x - \frac {1}{2} \right )}}{7744} + \frac {233 \log {\left (x + \frac {3}{5} \right )}}{9453125} - \frac {1}{4296875 x + 2578125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________