Optimal. Leaf size=44 \[ -\frac {65}{27 (3 x+2)}+\frac {4}{9 (3 x+2)^2}-\frac {7}{243 (3 x+2)^3}-\frac {50}{81} \log (3 x+2) \]
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Rubi [A] time = 0.02, antiderivative size = 44, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} -\frac {65}{27 (3 x+2)}+\frac {4}{9 (3 x+2)^2}-\frac {7}{243 (3 x+2)^3}-\frac {50}{81} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x) (3+5 x)^2}{(2+3 x)^4} \, dx &=\int \left (\frac {7}{27 (2+3 x)^4}-\frac {8}{3 (2+3 x)^3}+\frac {65}{9 (2+3 x)^2}-\frac {50}{27 (2+3 x)}\right ) \, dx\\ &=-\frac {7}{243 (2+3 x)^3}+\frac {4}{9 (2+3 x)^2}-\frac {65}{27 (2+3 x)}-\frac {50}{81} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 36, normalized size = 0.82 \begin {gather*} -\frac {5265 x^2+6696 x+150 (3 x+2)^3 \log (3 x+2)+2131}{243 (3 x+2)^3} \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) (3+5 x)^2}{(2+3 x)^4} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.19, size = 52, normalized size = 1.18 \begin {gather*} -\frac {5265 \, x^{2} + 150 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 6696 \, x + 2131}{243 \, {\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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giac [A] time = 1.20, size = 29, normalized size = 0.66 \begin {gather*} -\frac {5265 \, x^{2} + 6696 \, x + 2131}{243 \, {\left (3 \, x + 2\right )}^{3}} - \frac {50}{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 = 0.00, size = 37, normalized size = 0.84 \begin {gather*} -\frac {50 \ln \left (3 x +2\right )}{81}-\frac {7}{243 \left (3 x +2\right )^{3}}+\frac {4}{9 \left (3 x +2\right )^{2}}-\frac {65}{27 \left (3 x +2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 38, normalized size = 0.86 \begin {gather*} -\frac {5265 \, x^{2} + 6696 \, x + 2131}{243 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} - \frac {50}{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 = 0.04, size = 34, normalized size = 0.77 \begin {gather*} -\frac {50\,\ln \left (x+\frac {2}{3}\right )}{81}-\frac {\frac {65\,x^2}{81}+\frac {248\,x}{243}+\frac {2131}{6561}}{x^3+2\,x^2+\frac {4\,x}{3}+\frac {8}{27}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 36, normalized size = 0.82 \begin {gather*} - \frac {5265 x^{2} + 6696 x + 2131}{6561 x^{3} + 13122 x^{2} + 8748 x + 1944} - \frac {50 \log {\left (3 x + 2 \right )}}{81} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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