Optimal. Leaf size=66 \[ -\frac {1215 x^5}{8}-\frac {73305 x^4}{64}-\frac {69273 x^3}{16}-\frac {747297 x^2}{64}-\frac {3907293 x}{128}-\frac {6206585}{256 (1-2 x)}+\frac {2033647}{512 (1-2 x)^2}-\frac {8117095}{256} \log (1-2 x) \]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 66, 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 {1215 x^5}{8}-\frac {73305 x^4}{64}-\frac {69273 x^3}{16}-\frac {747297 x^2}{64}-\frac {3907293 x}{128}-\frac {6206585}{256 (1-2 x)}+\frac {2033647}{512 (1-2 x)^2}-\frac {8117095}{256} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^5 (3+5 x)^2}{(1-2 x)^3} \, dx &=\int \left (-\frac {3907293}{128}-\frac {747297 x}{32}-\frac {207819 x^2}{16}-\frac {73305 x^3}{16}-\frac {6075 x^4}{8}-\frac {2033647}{128 (-1+2 x)^3}-\frac {6206585}{128 (-1+2 x)^2}-\frac {8117095}{128 (-1+2 x)}\right ) \, dx\\ &=\frac {2033647}{512 (1-2 x)^2}-\frac {6206585}{256 (1-2 x)}-\frac {3907293 x}{128}-\frac {747297 x^2}{64}-\frac {69273 x^3}{16}-\frac {73305 x^4}{64}-\frac {1215 x^5}{8}-\frac {8117095}{256} \log (1-2 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 61, normalized size = 0.92 \begin {gather*} -\frac {622080 x^7+4069440 x^6+13197888 x^5+31266000 x^4+81639840 x^3-190079460 x^2+58608500 x+32468380 (1-2 x)^2 \log (1-2 x)+1508337}{1024 (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)^5 (3+5 x)^2}{(1-2 x)^3} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.04, size = 67, normalized size = 1.02 \begin {gather*} -\frac {311040 \, x^{7} + 2034720 \, x^{6} + 6598944 \, x^{5} + 15633000 \, x^{4} + 40819920 \, x^{3} - 56538312 \, x^{2} + 16234190 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 9197168 \, x + 10379523}{512 \, {\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 = 1.17, size = 47, normalized size = 0.71 \begin {gather*} -\frac {1215}{8} \, x^{5} - \frac {73305}{64} \, x^{4} - \frac {69273}{16} \, x^{3} - \frac {747297}{64} \, x^{2} - \frac {3907293}{128} \, x + \frac {26411 \, {\left (940 \, x - 393\right )}}{512 \, {\left (2 \, x - 1\right )}^{2}} - \frac {8117095}{256} \, \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 = 51, normalized size = 0.77 \begin {gather*} -\frac {1215 x^{5}}{8}-\frac {73305 x^{4}}{64}-\frac {69273 x^{3}}{16}-\frac {747297 x^{2}}{64}-\frac {3907293 x}{128}-\frac {8117095 \ln \left (2 x -1\right )}{256}+\frac {2033647}{512 \left (2 x -1\right )^{2}}+\frac {6206585}{256 \left (2 x -1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.49, size = 51, normalized size = 0.77 \begin {gather*} -\frac {1215}{8} \, x^{5} - \frac {73305}{64} \, x^{4} - \frac {69273}{16} \, x^{3} - \frac {747297}{64} \, x^{2} - \frac {3907293}{128} \, x + \frac {26411 \, {\left (940 \, x - 393\right )}}{512 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {8117095}{256} \, \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 = 46, normalized size = 0.70 \begin {gather*} \frac {\frac {6206585\,x}{512}-\frac {10379523}{2048}}{x^2-x+\frac {1}{4}}-\frac {8117095\,\ln \left (x-\frac {1}{2}\right )}{256}-\frac {3907293\,x}{128}-\frac {747297\,x^2}{64}-\frac {69273\,x^3}{16}-\frac {73305\,x^4}{64}-\frac {1215\,x^5}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.15, size = 58, normalized size = 0.88 \begin {gather*} - \frac {1215 x^{5}}{8} - \frac {73305 x^{4}}{64} - \frac {69273 x^{3}}{16} - \frac {747297 x^{2}}{64} - \frac {3907293 x}{128} - \frac {10379523 - 24826340 x}{2048 x^{2} - 2048 x + 512} - \frac {8117095 \log {\left (2 x - 1 \right )}}{256} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________