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 = 0.02, antiderivative size = 56, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} \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} \end {gather*}
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*}
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Mathematica [A] time = 0.01, size = 31, normalized size = 0.55 \begin {gather*} \frac {81000 x^4+132975 x^3+61938 x^2+642 x-3688}{2916 (3 x+2)^7} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1-2 x) (3+5 x)^3}{(2+3 x)^8} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.34, size = 59, normalized size = 1.05 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.19, size = 29, normalized size = 0.52 \begin {gather*} \frac {81000 \, x^{4} + 132975 \, x^{3} + 61938 \, x^{2} + 642 \, x - 3688}{2916 \, {\left (3 \, x + 2\right )}^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 47, normalized size = 0.84 \begin {gather*} \frac {1}{243 \left (3 x +2\right )^{7}}-\frac {107}{1458 \left (3 x +2\right )^{6}}+\frac {37}{81 \left (3 x +2\right )^{5}}-\frac {1025}{972 \left (3 x +2\right )^{4}}+\frac {250}{729 \left (3 x +2\right )^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 59, normalized size = 1.05 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.11, size = 46, normalized size = 0.82 \begin {gather*} \frac {250}{729\,{\left (3\,x+2\right )}^3}-\frac {1025}{972\,{\left (3\,x+2\right )}^4}+\frac {37}{81\,{\left (3\,x+2\right )}^5}-\frac {107}{1458\,{\left (3\,x+2\right )}^6}+\frac {1}{243\,{\left (3\,x+2\right )}^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 56, normalized size = 1.00 \begin {gather*} - \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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