Optimal. Leaf size=34 \[ \frac{5}{27 (3 x+2)^2}-\frac{37}{81 (3 x+2)^3}+\frac{7}{108 (3 x+2)^4} \]
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Rubi [A] time = 0.01388, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {77} \[ \frac{5}{27 (3 x+2)^2}-\frac{37}{81 (3 x+2)^3}+\frac{7}{108 (3 x+2)^4} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (3+5 x)}{(2+3 x)^5} \, dx &=\int \left (-\frac{7}{9 (2+3 x)^5}+\frac{37}{9 (2+3 x)^4}-\frac{10}{9 (2+3 x)^3}\right ) \, dx\\ &=\frac{7}{108 (2+3 x)^4}-\frac{37}{81 (2+3 x)^3}+\frac{5}{27 (2+3 x)^2}\\ \end{align*}
Mathematica [A] time = 0.0050599, size = 21, normalized size = 0.62 \[ \frac{540 x^2+276 x-35}{324 (3 x+2)^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 29, normalized size = 0.9 \begin{align*}{\frac{7}{108\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{37}{81\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{5}{27\, \left ( 2+3\,x \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.33924, size = 46, normalized size = 1.35 \begin{align*} \frac{540 \, x^{2} + 276 \, x - 35}{324 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4504, size = 96, normalized size = 2.82 \begin{align*} \frac{540 \, x^{2} + 276 \, x - 35}{324 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.126262, size = 29, normalized size = 0.85 \begin{align*} \frac{540 x^{2} + 276 x - 35}{26244 x^{4} + 69984 x^{3} + 69984 x^{2} + 31104 x + 5184} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.30621, size = 38, normalized size = 1.12 \begin{align*} \frac{5}{27 \,{\left (3 \, x + 2\right )}^{2}} - \frac{37}{81 \,{\left (3 \, x + 2\right )}^{3}} + \frac{7}{108 \,{\left (3 \, x + 2\right )}^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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