Optimal. Leaf size=45 \[ \frac {5929}{64 (1-2 x)^2}-\frac {1309}{4 (1-2 x)}-\frac {1815 x}{16}-\frac {225 x^2}{16}-\frac {3467}{16} \log (1-2 x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 45, 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 {225 x^2}{16}-\frac {1815 x}{16}-\frac {1309}{4 (1-2 x)}+\frac {5929}{64 (1-2 x)^2}-\frac {3467}{16} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^2 (3+5 x)^2}{(1-2 x)^3} \, dx &=\int \left (-\frac {1815}{16}-\frac {225 x}{8}-\frac {5929}{16 (-1+2 x)^3}-\frac {1309}{2 (-1+2 x)^2}-\frac {3467}{8 (-1+2 x)}\right ) \, dx\\ &=\frac {5929}{64 (1-2 x)^2}-\frac {1309}{4 (1-2 x)}-\frac {1815 x}{16}-\frac {225 x^2}{16}-\frac {3467}{16} \log (1-2 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 46, normalized size = 1.02 \begin {gather*} -\frac {2790-4802 x-10890 x^2+6360 x^3+900 x^4+3467 (1-2 x)^2 \log (1-2 x)}{16 (1-2 x)^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.10, size = 36, normalized size = 0.80
method | result | size |
risch | \(-\frac {225 x^{2}}{16}-\frac {1815 x}{16}+\frac {\frac {1309 x}{2}-\frac {15015}{64}}{\left (-1+2 x \right )^{2}}-\frac {3467 \ln \left (-1+2 x \right )}{16}\) | \(32\) |
default | \(-\frac {225 x^{2}}{16}-\frac {1815 x}{16}+\frac {1309}{4 \left (-1+2 x \right )}+\frac {5929}{64 \left (-1+2 x \right )^{2}}-\frac {3467 \ln \left (-1+2 x \right )}{16}\) | \(36\) |
norman | \(\frac {-\frac {3179}{8} x +\frac {11025}{8} x^{2}-\frac {795}{2} x^{3}-\frac {225}{4} x^{4}}{\left (-1+2 x \right )^{2}}-\frac {3467 \ln \left (-1+2 x \right )}{16}\) | \(37\) |
meijerg | \(\frac {18 x \left (2-2 x \right )}{\left (1-2 x \right )^{2}}+\frac {114 x^{2}}{\left (1-2 x \right )^{2}}-\frac {541 x \left (-18 x +6\right )}{24 \left (1-2 x \right )^{2}}-\frac {3467 \ln \left (1-2 x \right )}{16}-\frac {285 x \left (16 x^{2}-36 x +12\right )}{16 \left (1-2 x \right )^{2}}-\frac {45 x \left (40 x^{3}+80 x^{2}-180 x +60\right )}{32 \left (1-2 x \right )^{2}}\) | \(97\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 36, normalized size = 0.80 \begin {gather*} -\frac {225}{16} \, x^{2} - \frac {1815}{16} \, x + \frac {77 \, {\left (544 \, x - 195\right )}}{64 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {3467}{16} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.44, size = 52, normalized size = 1.16 \begin {gather*} -\frac {3600 \, x^{4} + 25440 \, x^{3} - 28140 \, x^{2} + 13868 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 34628 \, x + 15015}{64 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 37, normalized size = 0.82 \begin {gather*} - \frac {225 x^{2}}{16} - \frac {1815 x}{16} - \frac {15015 - 41888 x}{256 x^{2} - 256 x + 64} - \frac {3467 \log {\left (2 x - 1 \right )}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.51, size = 32, normalized size = 0.71 \begin {gather*} -\frac {225}{16} \, x^{2} - \frac {1815}{16} \, x + \frac {77 \, {\left (544 \, x - 195\right )}}{64 \, {\left (2 \, x - 1\right )}^{2}} - \frac {3467}{16} \, \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 = 0.03, size = 31, normalized size = 0.69 \begin {gather*} \frac {\frac {1309\,x}{8}-\frac {15015}{256}}{x^2-x+\frac {1}{4}}-\frac {3467\,\ln \left (x-\frac {1}{2}\right )}{16}-\frac {1815\,x}{16}-\frac {225\,x^2}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________