Optimal. Leaf size=59 \[ \frac {16253 x}{729}-\frac {1795 x^2}{81}+\frac {1700 x^3}{81}-\frac {250 x^4}{27}+\frac {343}{4374 (2+3 x)^2}-\frac {1813}{729 (2+3 x)}-\frac {10073}{729} \log (2+3 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 59, 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 {250 x^4}{27}+\frac {1700 x^3}{81}-\frac {1795 x^2}{81}+\frac {16253 x}{729}-\frac {1813}{729 (3 x+2)}+\frac {343}{4374 (3 x+2)^2}-\frac {10073}{729} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (3+5 x)^3}{(2+3 x)^3} \, dx &=\int \left (\frac {16253}{729}-\frac {3590 x}{81}+\frac {1700 x^2}{27}-\frac {1000 x^3}{27}-\frac {343}{729 (2+3 x)^3}+\frac {1813}{243 (2+3 x)^2}-\frac {10073}{243 (2+3 x)}\right ) \, dx\\ &=\frac {16253 x}{729}-\frac {1795 x^2}{81}+\frac {1700 x^3}{81}-\frac {250 x^4}{27}+\frac {343}{4374 (2+3 x)^2}-\frac {1813}{729 (2+3 x)}-\frac {10073}{729} \log (2+3 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 56, normalized size = 0.95 \begin {gather*} \frac {551755+2076942 x+2072124 x^2+81702 x^3+67230 x^4+340200 x^5-364500 x^6-60438 (2+3 x)^2 \log (2+3 x)}{4374 (2+3 x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 46, normalized size = 0.78
method | result | size |
risch | \(-\frac {250 x^{4}}{27}+\frac {1700 x^{3}}{81}-\frac {1795 x^{2}}{81}+\frac {16253 x}{729}+\frac {-\frac {1813 x}{243}-\frac {21413}{4374}}{\left (2+3 x \right )^{2}}-\frac {10073 \ln \left (2+3 x \right )}{729}\) | \(42\) |
default | \(\frac {16253 x}{729}-\frac {1795 x^{2}}{81}+\frac {1700 x^{3}}{81}-\frac {250 x^{4}}{27}+\frac {343}{4374 \left (2+3 x \right )^{2}}-\frac {1813}{729 \left (2+3 x \right )}-\frac {10073 \ln \left (2+3 x \right )}{729}\) | \(46\) |
norman | \(\frac {\frac {46853}{486} x +\frac {41021}{216} x^{2}+\frac {1513}{81} x^{3}+\frac {415}{27} x^{4}+\frac {700}{9} x^{5}-\frac {250}{3} x^{6}}{\left (2+3 x \right )^{2}}-\frac {10073 \ln \left (2+3 x \right )}{729}\) | \(47\) |
meijerg | \(\frac {27 x \left (\frac {3 x}{2}+2\right )}{16 \left (1+\frac {3 x}{2}\right )^{2}}-\frac {27 x^{2}}{16 \left (1+\frac {3 x}{2}\right )^{2}}+\frac {29 x \left (\frac {27 x}{2}+6\right )}{12 \left (1+\frac {3 x}{2}\right )^{2}}-\frac {10073 \ln \left (1+\frac {3 x}{2}\right )}{729}+\frac {179 x \left (9 x^{2}+27 x +12\right )}{108 \left (1+\frac {3 x}{2}\right )^{2}}-\frac {58 x \left (-\frac {135}{8} x^{3}+45 x^{2}+135 x +60\right )}{27 \left (1+\frac {3 x}{2}\right )^{2}}-\frac {200 x \left (\frac {81}{8} x^{4}-\frac {135}{8} x^{3}+45 x^{2}+135 x +60\right )}{243 \left (1+\frac {3 x}{2}\right )^{2}}+\frac {2000 x \left (-\frac {1701}{32} x^{5}+\frac {567}{8} x^{4}-\frac {945}{8} x^{3}+315 x^{2}+945 x +420\right )}{5103 \left (1+\frac {3 x}{2}\right )^{2}}\) | \(162\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 46, normalized size = 0.78 \begin {gather*} -\frac {250}{27} \, x^{4} + \frac {1700}{81} \, x^{3} - \frac {1795}{81} \, x^{2} + \frac {16253}{729} \, x - \frac {49 \, {\left (666 \, x + 437\right )}}{4374 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac {10073}{729} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 62, normalized size = 1.05 \begin {gather*} -\frac {364500 \, x^{6} - 340200 \, x^{5} - 67230 \, x^{4} - 81702 \, x^{3} - 782496 \, x^{2} + 60438 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 357438 \, x + 21413}{4374 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 49, normalized size = 0.83 \begin {gather*} - \frac {250 x^{4}}{27} + \frac {1700 x^{3}}{81} - \frac {1795 x^{2}}{81} + \frac {16253 x}{729} - \frac {32634 x + 21413}{39366 x^{2} + 52488 x + 17496} - \frac {10073 \log {\left (3 x + 2 \right )}}{729} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.33, size = 42, normalized size = 0.71 \begin {gather*} -\frac {250}{27} \, x^{4} + \frac {1700}{81} \, x^{3} - \frac {1795}{81} \, x^{2} + \frac {16253}{729} \, x - \frac {49 \, {\left (666 \, x + 437\right )}}{4374 \, {\left (3 \, x + 2\right )}^{2}} - \frac {10073}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 42, normalized size = 0.71 \begin {gather*} \frac {16253\,x}{729}-\frac {10073\,\ln \left (x+\frac {2}{3}\right )}{729}-\frac {\frac {1813\,x}{2187}+\frac {21413}{39366}}{x^2+\frac {4\,x}{3}+\frac {4}{9}}-\frac {1795\,x^2}{81}+\frac {1700\,x^3}{81}-\frac {250\,x^4}{27} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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