Optimal. Leaf size=56 \[ \frac{250}{729 (3 x+2)^3}-\frac{1025}{972 (3 x+2)^4}+\frac{37}{81 (3 x+2)^5}-\frac{107}{1458 (3 x+2)^6}+\frac{1}{243 (3 x+2)^7} \]
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Rubi [A] time = 0.0202537, antiderivative size = 56, 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} \[ \frac{250}{729 (3 x+2)^3}-\frac{1025}{972 (3 x+2)^4}+\frac{37}{81 (3 x+2)^5}-\frac{107}{1458 (3 x+2)^6}+\frac{1}{243 (3 x+2)^7} \]
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)^8} \, dx &=\int \left (-\frac{7}{81 (2+3 x)^8}+\frac{107}{81 (2+3 x)^7}-\frac{185}{27 (2+3 x)^6}+\frac{1025}{81 (2+3 x)^5}-\frac{250}{81 (2+3 x)^4}\right ) \, dx\\ &=\frac{1}{243 (2+3 x)^7}-\frac{107}{1458 (2+3 x)^6}+\frac{37}{81 (2+3 x)^5}-\frac{1025}{972 (2+3 x)^4}+\frac{250}{729 (2+3 x)^3}\\ \end{align*}
Mathematica [A] time = 0.0088406, size = 31, normalized size = 0.55 \[ \frac{81000 x^4+132975 x^3+61938 x^2+642 x-3688}{2916 (3 x+2)^7} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 47, normalized size = 0.8 \begin{align*}{\frac{1}{243\, \left ( 2+3\,x \right ) ^{7}}}-{\frac{107}{1458\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{37}{81\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{1025}{972\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{250}{729\, \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 = 1.20596, size = 80, normalized size = 1.43 \begin{align*} \frac{81000 \, x^{4} + 132975 \, x^{3} + 61938 \, x^{2} + 642 \, x - 3688}{2916 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4902, size = 196, normalized size = 3.5 \begin{align*} \frac{81000 \, x^{4} + 132975 \, x^{3} + 61938 \, x^{2} + 642 \, x - 3688}{2916 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.170886, size = 54, normalized size = 0.96 \begin{align*} \frac{81000 x^{4} + 132975 x^{3} + 61938 x^{2} + 642 x - 3688}{6377292 x^{7} + 29760696 x^{6} + 59521392 x^{5} + 66134880 x^{4} + 44089920 x^{3} + 17635968 x^{2} + 3919104 x + 373248} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.68227, size = 39, normalized size = 0.7 \begin{align*} \frac{81000 \, x^{4} + 132975 \, x^{3} + 61938 \, x^{2} + 642 \, x - 3688}{2916 \,{\left (3 \, x + 2\right )}^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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