Optimal. Leaf size=45 \[ \frac{50}{243 (3 x+2)^3}-\frac{65}{108 (3 x+2)^4}+\frac{8}{45 (3 x+2)^5}-\frac{7}{486 (3 x+2)^6} \]
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Rubi [A] time = 0.0167643, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ \frac{50}{243 (3 x+2)^3}-\frac{65}{108 (3 x+2)^4}+\frac{8}{45 (3 x+2)^5}-\frac{7}{486 (3 x+2)^6} \]
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)^7} \, dx &=\int \left (\frac{7}{27 (2+3 x)^7}-\frac{8}{3 (2+3 x)^6}+\frac{65}{9 (2+3 x)^5}-\frac{50}{27 (2+3 x)^4}\right ) \, dx\\ &=-\frac{7}{486 (2+3 x)^6}+\frac{8}{45 (2+3 x)^5}-\frac{65}{108 (2+3 x)^4}+\frac{50}{243 (2+3 x)^3}\\ \end{align*}
Mathematica [A] time = 0.0087142, size = 26, normalized size = 0.58 \[ \frac{27000 x^3+27675 x^2+3492 x-2042}{4860 (3 x+2)^6} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 38, normalized size = 0.8 \begin{align*} -{\frac{7}{486\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{8}{45\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{65}{108\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{50}{243\, \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 = 2.08019, size = 66, normalized size = 1.47 \begin{align*} \frac{27000 \, x^{3} + 27675 \, x^{2} + 3492 \, x - 2042}{4860 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.74405, size = 155, normalized size = 3.44 \begin{align*} \frac{27000 \, x^{3} + 27675 \, x^{2} + 3492 \, x - 2042}{4860 \,{\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.154109, size = 44, normalized size = 0.98 \begin{align*} \frac{27000 x^{3} + 27675 x^{2} + 3492 x - 2042}{3542940 x^{6} + 14171760 x^{5} + 23619600 x^{4} + 20995200 x^{3} + 10497600 x^{2} + 2799360 x + 311040} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.61151, size = 32, normalized size = 0.71 \begin{align*} \frac{27000 \, x^{3} + 27675 \, x^{2} + 3492 \, x - 2042}{4860 \,{\left (3 \, x + 2\right )}^{6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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