Optimal. Leaf size=48 \[ \frac {1271 x}{243}-\frac {305 x^2}{54}-\frac {800 x^3}{81}+\frac {125 x^4}{9}+\frac {49}{729 (2+3 x)}+\frac {763}{729} \log (2+3 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 48, 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 {125 x^4}{9}-\frac {800 x^3}{81}-\frac {305 x^2}{54}+\frac {1271 x}{243}+\frac {49}{729 (3 x+2)}+\frac {763}{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)^2 (3+5 x)^3}{(2+3 x)^2} \, dx &=\int \left (\frac {1271}{243}-\frac {305 x}{27}-\frac {800 x^2}{27}+\frac {500 x^3}{9}-\frac {49}{243 (2+3 x)^2}+\frac {763}{243 (2+3 x)}\right ) \, dx\\ &=\frac {1271 x}{243}-\frac {305 x^2}{54}-\frac {800 x^3}{81}+\frac {125 x^4}{9}+\frac {49}{729 (2+3 x)}+\frac {763}{729} \log (2+3 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 49, normalized size = 1.02 \begin {gather*} \frac {3158+50052 x+19224 x^2-160515 x^3-8100 x^4+182250 x^5+4578 (2+3 x) \log (20+30 x)}{4374 (2+3 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 37, normalized size = 0.77
method | result | size |
risch | \(\frac {125 x^{4}}{9}-\frac {800 x^{3}}{81}-\frac {305 x^{2}}{54}+\frac {1271 x}{243}+\frac {49}{2187 \left (\frac {2}{3}+x \right )}+\frac {763 \ln \left (2+3 x \right )}{729}\) | \(35\) |
default | \(\frac {1271 x}{243}-\frac {305 x^{2}}{54}-\frac {800 x^{3}}{81}+\frac {125 x^{4}}{9}+\frac {49}{729 \left (2+3 x \right )}+\frac {763 \ln \left (2+3 x \right )}{729}\) | \(37\) |
norman | \(\frac {\frac {5035}{486} x +\frac {356}{81} x^{2}-\frac {5945}{162} x^{3}-\frac {50}{27} x^{4}+\frac {125}{3} x^{5}}{2+3 x}+\frac {763 \ln \left (2+3 x \right )}{729}\) | \(42\) |
meijerg | \(\frac {9 x}{4 \left (1+\frac {3 x}{2}\right )}+\frac {763 \ln \left (1+\frac {3 x}{2}\right )}{729}-\frac {23 x \left (\frac {9 x}{2}+6\right )}{3 \left (1+\frac {3 x}{2}\right )}+\frac {235 x \left (-\frac {9}{2} x^{2}+9 x +12\right )}{54 \left (1+\frac {3 x}{2}\right )}+\frac {320 x \left (\frac {135}{8} x^{3}-\frac {45}{2} x^{2}+45 x +60\right )}{243 \left (1+\frac {3 x}{2}\right )}-\frac {1000 x \left (-\frac {243}{16} x^{4}+\frac {135}{8} x^{3}-\frac {45}{2} x^{2}+45 x +60\right )}{729 \left (1+\frac {3 x}{2}\right )}\) | \(110\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 36, normalized size = 0.75 \begin {gather*} \frac {125}{9} \, x^{4} - \frac {800}{81} \, x^{3} - \frac {305}{54} \, x^{2} + \frac {1271}{243} \, x + \frac {49}{729 \, {\left (3 \, x + 2\right )}} + \frac {763}{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 = 0.40, size = 47, normalized size = 0.98 \begin {gather*} \frac {60750 \, x^{5} - 2700 \, x^{4} - 53505 \, x^{3} + 6408 \, x^{2} + 1526 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 15252 \, x + 98}{1458 \, {\left (3 \, x + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 41, normalized size = 0.85 \begin {gather*} \frac {125 x^{4}}{9} - \frac {800 x^{3}}{81} - \frac {305 x^{2}}{54} + \frac {1271 x}{243} + \frac {763 \log {\left (3 x + 2 \right )}}{729} + \frac {49}{2187 x + 1458} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.68, size = 66, normalized size = 1.38 \begin {gather*} -\frac {1}{4374} \, {\left (3 \, x + 2\right )}^{4} {\left (\frac {7600}{3 \, x + 2} - \frac {24855}{{\left (3 \, x + 2\right )}^{2}} + \frac {24594}{{\left (3 \, x + 2\right )}^{3}} - 750\right )} + \frac {49}{729 \, {\left (3 \, x + 2\right )}} - \frac {763}{729} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 34, normalized size = 0.71 \begin {gather*} \frac {1271\,x}{243}+\frac {763\,\ln \left (x+\frac {2}{3}\right )}{729}+\frac {49}{2187\,\left (x+\frac {2}{3}\right )}-\frac {305\,x^2}{54}-\frac {800\,x^3}{81}+\frac {125\,x^4}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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