Optimal. Leaf size=56 \[ \frac {1780 x}{243}-\frac {100 x^2}{81}-\frac {343}{2187 (2+3 x)^3}+\frac {1862}{729 (2+3 x)^2}-\frac {11599}{729 (2+3 x)}-\frac {8198}{729} \log (2+3 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 56, 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 {100 x^2}{81}+\frac {1780 x}{243}-\frac {11599}{729 (3 x+2)}+\frac {1862}{729 (3 x+2)^2}-\frac {343}{2187 (3 x+2)^3}-\frac {8198}{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)^4} \, dx &=\int \left (\frac {1780}{243}-\frac {200 x}{81}+\frac {343}{243 (2+3 x)^4}-\frac {3724}{243 (2+3 x)^3}+\frac {11599}{243 (2+3 x)^2}-\frac {8198}{243 (2+3 x)}\right ) \, dx\\ &=\frac {1780 x}{243}-\frac {100 x^2}{81}-\frac {343}{2187 (2+3 x)^3}+\frac {1862}{729 (2+3 x)^2}-\frac {11599}{729 (2+3 x)}-\frac {8198}{729} \log (2+3 x)\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 51, normalized size = 0.91 \begin {gather*} \frac {-33319+155034 x+883467 x^2+1088640 x^3+286740 x^4-72900 x^5-24594 (2+3 x)^3 \log (20+30 x)}{2187 (2+3 x)^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 45, normalized size = 0.80
method | result | size |
risch | \(-\frac {100 x^{2}}{81}+\frac {1780 x}{243}+\frac {-\frac {11599}{81} x^{2}-\frac {44534}{243} x -\frac {128359}{2187}}{\left (2+3 x \right )^{3}}-\frac {8198 \ln \left (2+3 x \right )}{729}\) | \(37\) |
norman | \(\frac {\frac {67771}{486} x +\frac {164203}{324} x^{2}+\frac {355879}{648} x^{3}+\frac {1180}{9} x^{4}-\frac {100}{3} x^{5}}{\left (2+3 x \right )^{3}}-\frac {8198 \ln \left (2+3 x \right )}{729}\) | \(42\) |
default | \(\frac {1780 x}{243}-\frac {100 x^{2}}{81}-\frac {343}{2187 \left (2+3 x \right )^{3}}+\frac {1862}{729 \left (2+3 x \right )^{2}}-\frac {11599}{729 \left (2+3 x \right )}-\frac {8198 \ln \left (2+3 x \right )}{729}\) | \(45\) |
meijerg | \(\frac {3 x \left (\frac {9}{4} x^{2}+\frac {9}{2} x +3\right )}{16 \left (1+\frac {3 x}{2}\right )^{3}}-\frac {x^{2} \left (3+\frac {3 x}{2}\right )}{4 \left (1+\frac {3 x}{2}\right )^{3}}-\frac {47 x^{3}}{48 \left (1+\frac {3 x}{2}\right )^{3}}-\frac {23 x \left (\frac {99}{2} x^{2}+45 x +12\right )}{108 \left (1+\frac {3 x}{2}\right )^{3}}-\frac {8198 \ln \left (1+\frac {3 x}{2}\right )}{729}+\frac {4 x \left (\frac {405}{8} x^{3}+\frac {495}{2} x^{2}+225 x +60\right )}{81 \left (1+\frac {3 x}{2}\right )^{3}}+\frac {200 x \left (-\frac {243}{16} x^{4}+\frac {405}{8} x^{3}+\frac {495}{2} x^{2}+225 x +60\right )}{729 \left (1+\frac {3 x}{2}\right )^{3}}\) | \(134\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 46, normalized size = 0.82 \begin {gather*} -\frac {100}{81} \, x^{2} + \frac {1780}{243} \, x - \frac {7 \, {\left (44739 \, x^{2} + 57258 \, x + 18337\right )}}{2187 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} - \frac {8198}{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 = 0.38, size = 67, normalized size = 1.20 \begin {gather*} -\frac {72900 \, x^{5} - 286740 \, x^{4} - 767880 \, x^{3} - 241947 \, x^{2} + 24594 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 272646 \, x + 128359}{2187 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 46, normalized size = 0.82 \begin {gather*} - \frac {100 x^{2}}{81} + \frac {1780 x}{243} - \frac {313173 x^{2} + 400806 x + 128359}{59049 x^{3} + 118098 x^{2} + 78732 x + 17496} - \frac {8198 \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 = 1.38, size = 37, normalized size = 0.66 \begin {gather*} -\frac {100}{81} \, x^{2} + \frac {1780}{243} \, x - \frac {7 \, {\left (44739 \, x^{2} + 57258 \, x + 18337\right )}}{2187 \, {\left (3 \, x + 2\right )}^{3}} - \frac {8198}{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 = 0.04, size = 42, normalized size = 0.75 \begin {gather*} \frac {1780\,x}{243}-\frac {8198\,\ln \left (x+\frac {2}{3}\right )}{729}-\frac {\frac {11599\,x^2}{2187}+\frac {44534\,x}{6561}+\frac {128359}{59049}}{x^3+2\,x^2+\frac {4\,x}{3}+\frac {8}{27}}-\frac {100\,x^2}{81} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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