Optimal. Leaf size=45 \[ \frac {50 x^2}{27}-\frac {20 x}{3}+\frac {518}{243 (3 x+2)}-\frac {49}{486 (3 x+2)^2}+\frac {503}{81} \log (3 x+2) \]
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Rubi [A] time = 0.02, antiderivative size = 45, 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} \begin {gather*} \frac {50 x^2}{27}-\frac {20 x}{3}+\frac {518}{243 (3 x+2)}-\frac {49}{486 (3 x+2)^2}+\frac {503}{81} \log (3 x+2) \end {gather*}
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)^3} \, dx &=\int \left (-\frac {20}{3}+\frac {100 x}{27}+\frac {49}{81 (2+3 x)^3}-\frac {518}{81 (2+3 x)^2}+\frac {503}{27 (2+3 x)}\right ) \, dx\\ &=-\frac {20 x}{3}+\frac {50 x^2}{27}-\frac {49}{486 (2+3 x)^2}+\frac {518}{243 (2+3 x)}+\frac {503}{81} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 42, normalized size = 0.93 \begin {gather*} \frac {503}{81} \log (3 x+2)-\frac {-900 x^4+2040 x^3+6480 x^2+4508 x+913}{54 (3 x+2)^2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1-2 x)^2 (3+5 x)^2}{(2+3 x)^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.72, size = 52, normalized size = 1.16 \begin {gather*} \frac {8100 \, x^{4} - 18360 \, x^{3} - 35280 \, x^{2} + 3018 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 9852 \, x + 2023}{486 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.81, size = 32, normalized size = 0.71 \begin {gather*} \frac {50}{27} \, x^{2} - \frac {20}{3} \, x + \frac {7 \, {\left (444 \, x + 289\right )}}{486 \, {\left (3 \, x + 2\right )}^{2}} + \frac {503}{81} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 36, normalized size = 0.80 \begin {gather*} \frac {50 x^{2}}{27}-\frac {20 x}{3}+\frac {503 \ln \left (3 x +2\right )}{81}-\frac {49}{486 \left (3 x +2\right )^{2}}+\frac {518}{243 \left (3 x +2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 36, normalized size = 0.80 \begin {gather*} \frac {50}{27} \, x^{2} - \frac {20}{3} \, x + \frac {7 \, {\left (444 \, x + 289\right )}}{486 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac {503}{81} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 31, normalized size = 0.69 \begin {gather*} \frac {503\,\ln \left (x+\frac {2}{3}\right )}{81}-\frac {20\,x}{3}+\frac {\frac {518\,x}{729}+\frac {2023}{4374}}{x^2+\frac {4\,x}{3}+\frac {4}{9}}+\frac {50\,x^2}{27} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 36, normalized size = 0.80 \begin {gather*} \frac {50 x^{2}}{27} - \frac {20 x}{3} + \frac {3108 x + 2023}{4374 x^{2} + 5832 x + 1944} + \frac {503 \log {\left (3 x + 2 \right )}}{81} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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