Optimal. Leaf size=41 \[ \frac {100 x^3}{27}-\frac {170 x^2}{27}+\frac {143 x}{27}-\frac {49}{243 (3 x+2)}-\frac {518}{243} \log (3 x+2) \]
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Rubi [A] time = 0.02, antiderivative size = 41, 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 = {88} \[ \frac {100 x^3}{27}-\frac {170 x^2}{27}+\frac {143 x}{27}-\frac {49}{243 (3 x+2)}-\frac {518}{243} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (3+5 x)^2}{(2+3 x)^2} \, dx &=\int \left (\frac {143}{27}-\frac {340 x}{27}+\frac {100 x^2}{9}+\frac {49}{81 (2+3 x)^2}-\frac {518}{81 (2+3 x)}\right ) \, dx\\ &=\frac {143 x}{27}-\frac {170 x^2}{27}+\frac {100 x^3}{27}-\frac {49}{243 (2+3 x)}-\frac {518}{243} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 44, normalized size = 1.07 \[ \frac {8100 x^4-8370 x^3+2403 x^2+23964 x-1554 (3 x+2) \log (3 x+2)+10681}{729 (3 x+2)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.94, size = 42, normalized size = 1.02 \[ \frac {2700 \, x^{4} - 2790 \, x^{3} + 801 \, x^{2} - 518 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 2574 \, x - 49}{243 \, {\left (3 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 57, normalized size = 1.39 \[ -\frac {1}{729} \, {\left (3 \, x + 2\right )}^{3} {\left (\frac {1110}{3 \, x + 2} - \frac {4527}{{\left (3 \, x + 2\right )}^{2}} - 100\right )} - \frac {49}{243 \, {\left (3 \, x + 2\right )}} + \frac {518}{243} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 32, normalized size = 0.78 \[ \frac {100 x^{3}}{27}-\frac {170 x^{2}}{27}+\frac {143 x}{27}-\frac {518 \ln \left (3 x +2\right )}{243}-\frac {49}{243 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 31, normalized size = 0.76 \[ \frac {100}{27} \, x^{3} - \frac {170}{27} \, x^{2} + \frac {143}{27} \, x - \frac {49}{243 \, {\left (3 \, x + 2\right )}} - \frac {518}{243} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 29, normalized size = 0.71 \[ \frac {143\,x}{27}-\frac {518\,\ln \left (x+\frac {2}{3}\right )}{243}-\frac {49}{729\,\left (x+\frac {2}{3}\right )}-\frac {170\,x^2}{27}+\frac {100\,x^3}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 34, normalized size = 0.83 \[ \frac {100 x^{3}}{27} - \frac {170 x^{2}}{27} + \frac {143 x}{27} - \frac {518 \log {\left (3 x + 2 \right )}}{243} - \frac {49}{729 x + 486} \]
Verification of antiderivative is not currently implemented for this CAS.
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