Optimal. Leaf size=45 \[ \frac {3773}{64 (1-2 x)^2}-\frac {3283}{16 (1-2 x)}-\frac {1107 x}{16}-\frac {135 x^2}{16}-\frac {1071}{8} \log (1-2 x) \]
[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 = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} -\frac {135 x^2}{16}-\frac {1107 x}{16}-\frac {3283}{16 (1-2 x)}+\frac {3773}{64 (1-2 x)^2}-\frac {1071}{8} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 78
Rubi steps
\begin {align*} \int \frac {(2+3 x)^3 (3+5 x)}{(1-2 x)^3} \, dx &=\int \left (-\frac {1107}{16}-\frac {135 x}{8}-\frac {3773}{16 (-1+2 x)^3}-\frac {3283}{8 (-1+2 x)^2}-\frac {1071}{4 (-1+2 x)}\right ) \, dx\\ &=\frac {3773}{64 (1-2 x)^2}-\frac {3283}{16 (1-2 x)}-\frac {1107 x}{16}-\frac {135 x^2}{16}-\frac {1071}{8} \log (1-2 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 46, normalized size = 1.02 \begin {gather*} -\frac {3505-6220 x-13284 x^2+7776 x^3+1080 x^4+4284 (1-2 x)^2 \log (1-2 x)}{32 (1-2 x)^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.08, size = 36, normalized size = 0.80
method | result | size |
risch | \(-\frac {135 x^{2}}{16}-\frac {1107 x}{16}+\frac {\frac {3283 x}{8}-\frac {9359}{64}}{\left (-1+2 x \right )^{2}}-\frac {1071 \ln \left (-1+2 x \right )}{8}\) | \(32\) |
default | \(-\frac {135 x^{2}}{16}-\frac {1107 x}{16}+\frac {3283}{16 \left (-1+2 x \right )}+\frac {3773}{64 \left (-1+2 x \right )^{2}}-\frac {1071 \ln \left (-1+2 x \right )}{8}\) | \(36\) |
norman | \(\frac {-\frac {975}{4} x +\frac {3413}{4} x^{2}-243 x^{3}-\frac {135}{4} x^{4}}{\left (-1+2 x \right )^{2}}-\frac {1071 \ln \left (-1+2 x \right )}{8}\) | \(37\) |
meijerg | \(\frac {12 x \left (2-2 x \right )}{\left (1-2 x \right )^{2}}+\frac {74 x^{2}}{\left (1-2 x \right )^{2}}-\frac {57 x \left (-18 x +6\right )}{4 \left (1-2 x \right )^{2}}-\frac {1071 \ln \left (1-2 x \right )}{8}-\frac {351 x \left (16 x^{2}-36 x +12\right )}{32 \left (1-2 x \right )^{2}}-\frac {27 x \left (40 x^{3}+80 x^{2}-180 x +60\right )}{32 \left (1-2 x \right )^{2}}\) | \(97\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.38, size = 36, normalized size = 0.80 \begin {gather*} -\frac {135}{16} \, x^{2} - \frac {1107}{16} \, x + \frac {49 \, {\left (536 \, x - 191\right )}}{64 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {1071}{8} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.42, size = 52, normalized size = 1.16 \begin {gather*} -\frac {2160 \, x^{4} + 15552 \, x^{3} - 17172 \, x^{2} + 8568 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 21836 \, x + 9359}{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 = 0.06, size = 37, normalized size = 0.82 \begin {gather*} - \frac {135 x^{2}}{16} - \frac {1107 x}{16} - \frac {9359 - 26264 x}{256 x^{2} - 256 x + 64} - \frac {1071 \log {\left (2 x - 1 \right )}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.83, size = 32, normalized size = 0.71 \begin {gather*} -\frac {135}{16} \, x^{2} - \frac {1107}{16} \, x + \frac {49 \, {\left (536 \, x - 191\right )}}{64 \, {\left (2 \, x - 1\right )}^{2}} - \frac {1071}{8} \, \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 {3283\,x}{32}-\frac {9359}{256}}{x^2-x+\frac {1}{4}}-\frac {1071\,\ln \left (x-\frac {1}{2}\right )}{8}-\frac {1107\,x}{16}-\frac {135\,x^2}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________