Optimal. Leaf size=49 \[ -\frac {250 x}{81}+\frac {185}{81 (3 x+2)}-\frac {107}{486 (3 x+2)^2}+\frac {7}{729 (3 x+2)^3}+\frac {1025}{243} \log (3 x+2) \]
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Rubi [A] time = 0.02, antiderivative size = 49, 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 {250 x}{81}+\frac {185}{81 (3 x+2)}-\frac {107}{486 (3 x+2)^2}+\frac {7}{729 (3 x+2)^3}+\frac {1025}{243} \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)^3}{(2+3 x)^4} \, dx &=\int \left (-\frac {250}{81}-\frac {7}{81 (2+3 x)^4}+\frac {107}{81 (2+3 x)^3}-\frac {185}{27 (2+3 x)^2}+\frac {1025}{81 (2+3 x)}\right ) \, dx\\ &=-\frac {250 x}{81}+\frac {7}{729 (2+3 x)^3}-\frac {107}{486 (2+3 x)^2}+\frac {185}{81 (2+3 x)}+\frac {1025}{243} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 47, normalized size = 0.96 \begin {gather*} \frac {-1500 (3 x+2)+\frac {3330}{3 x+2}-\frac {321}{(3 x+2)^2}+\frac {14}{(3 x+2)^3}+6150 \log (3 x+2)}{1458} \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)^3}{(2+3 x)^4} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.35, size = 62, normalized size = 1.27 \begin {gather*} -\frac {121500 \, x^{4} + 243000 \, x^{3} + 132030 \, x^{2} - 6150 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 2997 \, x - 12692}{1458 \, {\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 = 1.11, size = 32, normalized size = 0.65 \begin {gather*} -\frac {250}{81} \, x + \frac {29970 \, x^{2} + 38997 \, x + 12692}{1458 \, {\left (3 \, x + 2\right )}^{3}} + \frac {1025}{243} \, \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 = 40, normalized size = 0.82 \begin {gather*} -\frac {250 x}{81}+\frac {1025 \ln \left (3 x +2\right )}{243}+\frac {7}{729 \left (3 x +2\right )^{3}}-\frac {107}{486 \left (3 x +2\right )^{2}}+\frac {185}{81 \left (3 x +2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 41, normalized size = 0.84 \begin {gather*} -\frac {250}{81} \, x + \frac {29970 \, x^{2} + 38997 \, x + 12692}{1458 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac {1025}{243} \, \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 = 36, normalized size = 0.73 \begin {gather*} \frac {1025\,\ln \left (x+\frac {2}{3}\right )}{243}-\frac {250\,x}{81}+\frac {\frac {185\,x^2}{243}+\frac {4333\,x}{4374}+\frac {6346}{19683}}{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 = 41, normalized size = 0.84 \begin {gather*} - \frac {250 x}{81} - \frac {- 29970 x^{2} - 38997 x - 12692}{39366 x^{3} + 78732 x^{2} + 52488 x + 11664} + \frac {1025 \log {\left (3 x + 2 \right )}}{243} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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