Optimal. Leaf size=34 \[ \frac{10}{81 (3 x+2)^3}-\frac{37}{108 (3 x+2)^4}+\frac{7}{135 (3 x+2)^5} \]
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Rubi [A] time = 0.0143678, 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} \[ \frac{10}{81 (3 x+2)^3}-\frac{37}{108 (3 x+2)^4}+\frac{7}{135 (3 x+2)^5} \]
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)^6} \, dx &=\int \left (-\frac{7}{9 (2+3 x)^6}+\frac{37}{9 (2+3 x)^5}-\frac{10}{9 (2+3 x)^4}\right ) \, dx\\ &=\frac{7}{135 (2+3 x)^5}-\frac{37}{108 (2+3 x)^4}+\frac{10}{81 (2+3 x)^3}\\ \end{align*}
Mathematica [A] time = 0.0065319, size = 21, normalized size = 0.62 \[ \frac{1800 x^2+735 x-226}{1620 (3 x+2)^5} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 29, normalized size = 0.9 \begin{align*}{\frac{7}{135\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{37}{108\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{10}{81\, \left ( 2+3\,x \right ) ^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.17689, size = 53, normalized size = 1.56 \begin{align*} \frac{1800 \, x^{2} + 735 \, x - 226}{1620 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.44389, size = 117, normalized size = 3.44 \begin{align*} \frac{1800 \, x^{2} + 735 \, x - 226}{1620 \,{\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.13582, size = 34, normalized size = 1. \begin{align*} \frac{1800 x^{2} + 735 x - 226}{393660 x^{5} + 1312200 x^{4} + 1749600 x^{3} + 1166400 x^{2} + 388800 x + 51840} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.04798, size = 26, normalized size = 0.76 \begin{align*} \frac{1800 \, x^{2} + 735 \, x - 226}{1620 \,{\left (3 \, x + 2\right )}^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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