Optimal. Leaf size=34 \[ \frac{10}{27 (3 x+2)}-\frac{37}{54 (3 x+2)^2}+\frac{7}{81 (3 x+2)^3} \]
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Rubi [A] time = 0.0131873, 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} \[ \frac{10}{27 (3 x+2)}-\frac{37}{54 (3 x+2)^2}+\frac{7}{81 (3 x+2)^3} \]
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)^4} \, dx &=\int \left (-\frac{7}{9 (2+3 x)^4}+\frac{37}{9 (2+3 x)^3}-\frac{10}{9 (2+3 x)^2}\right ) \, dx\\ &=\frac{7}{81 (2+3 x)^3}-\frac{37}{54 (2+3 x)^2}+\frac{10}{27 (2+3 x)}\\ \end{align*}
Mathematica [A] time = 0.0057269, size = 21, normalized size = 0.62 \[ \frac{540 x^2+387 x+32}{162 (3 x+2)^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 29, normalized size = 0.9 \begin{align*}{\frac{7}{81\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{37}{54\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{10}{54+81\,x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.12632, size = 39, normalized size = 1.15 \begin{align*} \frac{540 \, x^{2} + 387 \, x + 32}{162 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4935, size = 80, normalized size = 2.35 \begin{align*} \frac{540 \, x^{2} + 387 \, x + 32}{162 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.114882, size = 24, normalized size = 0.71 \begin{align*} \frac{540 x^{2} + 387 x + 32}{4374 x^{3} + 8748 x^{2} + 5832 x + 1296} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.07519, size = 26, normalized size = 0.76 \begin{align*} \frac{540 \, x^{2} + 387 \, x + 32}{162 \,{\left (3 \, x + 2\right )}^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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