Optimal. Leaf size=50 \[ -\frac {135 x^3}{8}-\frac {3861 x^2}{32}-540 x-\frac {57281}{64 (1-2 x)}+\frac {26411}{128 (1-2 x)^2}-\frac {24843}{32} \log (1-2 x) \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 50, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} -\frac {135 x^3}{8}-\frac {3861 x^2}{32}-540 x-\frac {57281}{64 (1-2 x)}+\frac {26411}{128 (1-2 x)^2}-\frac {24843}{32} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x)^4 (3+5 x)}{(1-2 x)^3} \, dx &=\int \left (-540-\frac {3861 x}{16}-\frac {405 x^2}{8}-\frac {26411}{32 (-1+2 x)^3}-\frac {57281}{32 (-1+2 x)^2}-\frac {24843}{16 (-1+2 x)}\right ) \, dx\\ &=\frac {26411}{128 (1-2 x)^2}-\frac {57281}{64 (1-2 x)}-540 x-\frac {3861 x^2}{32}-\frac {135 x^3}{8}-\frac {24843}{32} \log (1-2 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 51, normalized size = 1.02 \begin {gather*} -\frac {2160 x^5+13284 x^4+54216 x^3-103950 x^2-1310 x+24843 (1-2 x)^2 \log (1-2 x)+12365}{32 (1-2 x)^2} \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 (3+5 x)}{(1-2 x)^3} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.58, size = 57, normalized size = 1.14 \begin {gather*} -\frac {8640 \, x^{5} + 53136 \, x^{4} + 216864 \, x^{3} - 261036 \, x^{2} + 99372 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 160004 \, x + 88151}{128 \, {\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 = 1.18, size = 37, normalized size = 0.74 \begin {gather*} -\frac {135}{8} \, x^{3} - \frac {3861}{32} \, x^{2} - 540 \, x + \frac {343 \, {\left (668 \, x - 257\right )}}{128 \, {\left (2 \, x - 1\right )}^{2}} - \frac {24843}{32} \, \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 = 41, normalized size = 0.82 \begin {gather*} -\frac {135 x^{3}}{8}-\frac {3861 x^{2}}{32}-540 x -\frac {24843 \ln \left (2 x -1\right )}{32}+\frac {26411}{128 \left (2 x -1\right )^{2}}+\frac {57281}{64 \left (2 x -1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.53, size = 41, normalized size = 0.82 \begin {gather*} -\frac {135}{8} \, x^{3} - \frac {3861}{32} \, x^{2} - 540 \, x + \frac {343 \, {\left (668 \, x - 257\right )}}{128 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {24843}{32} \, \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 = 36, normalized size = 0.72 \begin {gather*} \frac {\frac {57281\,x}{128}-\frac {88151}{512}}{x^2-x+\frac {1}{4}}-\frac {24843\,\ln \left (x-\frac {1}{2}\right )}{32}-540\,x-\frac {3861\,x^2}{32}-\frac {135\,x^3}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.13, size = 42, normalized size = 0.84 \begin {gather*} - \frac {135 x^{3}}{8} - \frac {3861 x^{2}}{32} - 540 x - \frac {88151 - 229124 x}{512 x^{2} - 512 x + 128} - \frac {24843 \log {\left (2 x - 1 \right )}}{32} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________