Optimal. Leaf size=52 \[ -\frac {1546 x}{81}+\frac {230 x^2}{27}-\frac {200 x^3}{81}-\frac {343}{1458 (2+3 x)^2}+\frac {3724}{729 (2+3 x)}+\frac {11599}{729} \log (2+3 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 52, 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 {200 x^3}{81}+\frac {230 x^2}{27}-\frac {1546 x}{81}+\frac {3724}{729 (3 x+2)}-\frac {343}{1458 (3 x+2)^2}+\frac {11599}{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)^2}{(2+3 x)^3} \, dx &=\int \left (-\frac {1546}{81}+\frac {460 x}{27}-\frac {200 x^2}{27}+\frac {343}{243 (2+3 x)^3}-\frac {3724}{243 (2+3 x)^2}+\frac {11599}{243 (2+3 x)}\right ) \, dx\\ &=-\frac {1546 x}{81}+\frac {230 x^2}{27}-\frac {200 x^3}{81}-\frac {343}{1458 (2+3 x)^2}+\frac {3724}{729 (2+3 x)}+\frac {11599}{729} \log (2+3 x)\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 51, normalized size = 0.98 \begin {gather*} -\frac {258005+1171896 x+1531512 x^2+347436 x^3-205740 x^4+97200 x^5-69594 (2+3 x)^2 \log (20+30 x)}{4374 (2+3 x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 41, normalized size = 0.79
method | result | size |
risch | \(-\frac {200 x^{3}}{81}+\frac {230 x^{2}}{27}-\frac {1546 x}{81}+\frac {\frac {3724 x}{243}+\frac {539}{54}}{\left (2+3 x \right )^{2}}+\frac {11599 \ln \left (2+3 x \right )}{729}\) | \(37\) |
default | \(-\frac {1546 x}{81}+\frac {230 x^{2}}{27}-\frac {200 x^{3}}{81}-\frac {343}{1458 \left (2+3 x \right )^{2}}+\frac {3724}{729 \left (2+3 x \right )}+\frac {11599 \ln \left (2+3 x \right )}{729}\) | \(41\) |
norman | \(\frac {-\frac {44209}{486} x -\frac {46963}{216} x^{2}-\frac {6434}{81} x^{3}+\frac {1270}{27} x^{4}-\frac {200}{9} x^{5}}{\left (2+3 x \right )^{2}}+\frac {11599 \ln \left (2+3 x \right )}{729}\) | \(42\) |
meijerg | \(\frac {9 x \left (\frac {3 x}{2}+2\right )}{16 \left (1+\frac {3 x}{2}\right )^{2}}-\frac {3 x^{2}}{2 \left (1+\frac {3 x}{2}\right )^{2}}+\frac {47 x \left (\frac {27 x}{2}+6\right )}{108 \left (1+\frac {3 x}{2}\right )^{2}}+\frac {11599 \ln \left (1+\frac {3 x}{2}\right )}{729}+\frac {23 x \left (9 x^{2}+27 x +12\right )}{18 \left (1+\frac {3 x}{2}\right )^{2}}-\frac {4 x \left (-\frac {135}{8} x^{3}+45 x^{2}+135 x +60\right )}{27 \left (1+\frac {3 x}{2}\right )^{2}}-\frac {400 x \left (\frac {81}{8} x^{4}-\frac {135}{8} x^{3}+45 x^{2}+135 x +60\right )}{729 \left (1+\frac {3 x}{2}\right )^{2}}\) | \(127\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.40, size = 41, normalized size = 0.79 \begin {gather*} -\frac {200}{81} \, x^{3} + \frac {230}{27} \, x^{2} - \frac {1546}{81} \, x + \frac {49 \, {\left (152 \, x + 99\right )}}{486 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac {11599}{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 = 0.42, size = 57, normalized size = 1.10 \begin {gather*} -\frac {32400 \, x^{5} - 68580 \, x^{4} + 115812 \, x^{3} + 284256 \, x^{2} - 23198 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 88968 \, x - 14553}{1458 \, {\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 = 0.11, size = 44, normalized size = 0.85 \begin {gather*} - \frac {200 x^{3}}{81} + \frac {230 x^{2}}{27} - \frac {1546 x}{81} - \frac {- 7448 x - 4851}{4374 x^{2} + 5832 x + 1944} + \frac {11599 \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 = 1.08, size = 37, normalized size = 0.71 \begin {gather*} -\frac {200}{81} \, x^{3} + \frac {230}{27} \, x^{2} - \frac {1546}{81} \, x + \frac {49 \, {\left (152 \, x + 99\right )}}{486 \, {\left (3 \, x + 2\right )}^{2}} + \frac {11599}{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 = 36, normalized size = 0.69 \begin {gather*} \frac {11599\,\ln \left (x+\frac {2}{3}\right )}{729}-\frac {1546\,x}{81}+\frac {\frac {3724\,x}{2187}+\frac {539}{486}}{x^2+\frac {4\,x}{3}+\frac {4}{9}}+\frac {230\,x^2}{27}-\frac {200\,x^3}{81} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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