Optimal. Leaf size=48 \[ \frac {1125 x^4}{16}+\frac {775 x^3}{2}+\frac {35135 x^2}{32}+\frac {41537 x}{16}+\frac {65219}{64 (1-2 x)}+\frac {144837}{64} \log (1-2 x) \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 48, 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 {1125 x^4}{16}+\frac {775 x^3}{2}+\frac {35135 x^2}{32}+\frac {41537 x}{16}+\frac {65219}{64 (1-2 x)}+\frac {144837}{64} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^2 (3+5 x)^3}{(1-2 x)^2} \, dx &=\int \left (\frac {41537}{16}+\frac {35135 x}{16}+\frac {2325 x^2}{2}+\frac {1125 x^3}{4}+\frac {65219}{32 (-1+2 x)^2}+\frac {144837}{32 (-1+2 x)}\right ) \, dx\\ &=\frac {65219}{64 (1-2 x)}+\frac {41537 x}{16}+\frac {35135 x^2}{32}+\frac {775 x^3}{2}+\frac {1125 x^4}{16}+\frac {144837}{64} \log (1-2 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 49, normalized size = 1.02 \begin {gather*} \frac {36000 x^5+180400 x^4+462960 x^3+1048104 x^2-1496774 x+579348 (2 x-1) \log (1-2 x)+155215}{256 (2 x-1)} \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)^2 (3+5 x)^3}{(1-2 x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.92, size = 47, normalized size = 0.98 \begin {gather*} \frac {9000 \, x^{5} + 45100 \, x^{4} + 115740 \, x^{3} + 262026 \, x^{2} + 144837 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 166148 \, x - 65219}{64 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.15, size = 66, normalized size = 1.38 \begin {gather*} \frac {1}{256} \, {\left (2 \, x - 1\right )}^{4} {\left (\frac {16900}{2 \, x - 1} + \frac {114220}{{\left (2 \, x - 1\right )}^{2}} + \frac {514536}{{\left (2 \, x - 1\right )}^{3}} + 1125\right )} - \frac {65219}{64 \, {\left (2 \, x - 1\right )}} - \frac {144837}{64} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 37, normalized size = 0.77 \begin {gather*} \frac {1125 x^{4}}{16}+\frac {775 x^{3}}{2}+\frac {35135 x^{2}}{32}+\frac {41537 x}{16}+\frac {144837 \ln \left (2 x -1\right )}{64}-\frac {65219}{64 \left (2 x -1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.59, size = 36, normalized size = 0.75 \begin {gather*} \frac {1125}{16} \, x^{4} + \frac {775}{2} \, x^{3} + \frac {35135}{32} \, x^{2} + \frac {41537}{16} \, x - \frac {65219}{64 \, {\left (2 \, x - 1\right )}} + \frac {144837}{64} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 34, normalized size = 0.71 \begin {gather*} \frac {41537\,x}{16}+\frac {144837\,\ln \left (x-\frac {1}{2}\right )}{64}-\frac {65219}{128\,\left (x-\frac {1}{2}\right )}+\frac {35135\,x^2}{32}+\frac {775\,x^3}{2}+\frac {1125\,x^4}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 41, normalized size = 0.85 \begin {gather*} \frac {1125 x^{4}}{16} + \frac {775 x^{3}}{2} + \frac {35135 x^{2}}{32} + \frac {41537 x}{16} + \frac {144837 \log {\left (2 x - 1 \right )}}{64} - \frac {65219}{128 x - 64} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________