Optimal. Leaf size=48 \[ -\frac {81 x}{40}-\frac {33271}{1936 (1-2 x)}+\frac {2401}{352 (1-2 x)^2}-\frac {153811 \log (1-2 x)}{21296}+\frac {\log (5 x+3)}{33275} \]
________________________________________________________________________________________
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 {81 x}{40}-\frac {33271}{1936 (1-2 x)}+\frac {2401}{352 (1-2 x)^2}-\frac {153811 \log (1-2 x)}{21296}+\frac {\log (5 x+3)}{33275} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^4}{(1-2 x)^3 (3+5 x)} \, dx &=\int \left (-\frac {81}{40}-\frac {2401}{88 (-1+2 x)^3}-\frac {33271}{968 (-1+2 x)^2}-\frac {153811}{10648 (-1+2 x)}+\frac {1}{6655 (3+5 x)}\right ) \, dx\\ &=\frac {2401}{352 (1-2 x)^2}-\frac {33271}{1936 (1-2 x)}-\frac {81 x}{40}-\frac {153811 \log (1-2 x)}{21296}+\frac {\log (3+5 x)}{33275}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.04, size = 46, normalized size = 0.96 \begin {gather*} \frac {-431244 (5 x+3)+\frac {18299050}{2 x-1}+\frac {7263025}{(1-2 x)^2}-7690550 \log (5-10 x)+32 \log (5 x+3)}{1064800} \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)^4}{(1-2 x)^3 (3+5 x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.46, size = 65, normalized size = 1.35 \begin {gather*} -\frac {8624880 \, x^{3} - 8624880 \, x^{2} - 32 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) + 7690550 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 34441880 \, x + 11036025}{1064800 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.16, size = 36, normalized size = 0.75 \begin {gather*} -\frac {81}{40} \, x + \frac {343 \, {\left (388 \, x - 117\right )}}{3872 \, {\left (2 \, x - 1\right )}^{2}} + \frac {1}{33275} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {153811}{21296} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 39, normalized size = 0.81 \begin {gather*} -\frac {81 x}{40}-\frac {153811 \ln \left (2 x -1\right )}{21296}+\frac {\ln \left (5 x +3\right )}{33275}+\frac {2401}{352 \left (2 x -1\right )^{2}}+\frac {33271}{1936 \left (2 x -1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.55, size = 39, normalized size = 0.81 \begin {gather*} -\frac {81}{40} \, x + \frac {343 \, {\left (388 \, x - 117\right )}}{3872 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac {1}{33275} \, \log \left (5 \, x + 3\right ) - \frac {153811}{21296} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.07, size = 32, normalized size = 0.67 \begin {gather*} \frac {\ln \left (x+\frac {3}{5}\right )}{33275}-\frac {153811\,\ln \left (x-\frac {1}{2}\right )}{21296}-\frac {81\,x}{40}+\frac {\frac {33271\,x}{3872}-\frac {40131}{15488}}{x^2-x+\frac {1}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.18, size = 37, normalized size = 0.77 \begin {gather*} - \frac {81 x}{40} - \frac {40131 - 133084 x}{15488 x^{2} - 15488 x + 3872} - \frac {153811 \log {\left (x - \frac {1}{2} \right )}}{21296} + \frac {\log {\left (x + \frac {3}{5} \right )}}{33275} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________