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 = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.00, 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} \begin {gather*} \frac {10}{27 (3 x+2)}-\frac {37}{54 (3 x+2)^2}+\frac {7}{81 (3 x+2)^3} \end {gather*}
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*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 0.62 \begin {gather*} \frac {540 x^2+387 x+32}{162 (3 x+2)^3} \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)}{(2+3 x)^4} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.24, size = 29, normalized size = 0.85 \begin {gather*} \frac {540 \, x^{2} + 387 \, x + 32}{162 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.32, size = 19, normalized size = 0.56 \begin {gather*} \frac {540 \, x^{2} + 387 \, x + 32}{162 \, {\left (3 \, x + 2\right )}^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 29, normalized size = 0.85 \begin {gather*} \frac {7}{81 \left (3 x +2\right )^{3}}-\frac {37}{54 \left (3 x +2\right )^{2}}+\frac {10}{27 \left (3 x +2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 29, normalized size = 0.85 \begin {gather*} \frac {540 \, x^{2} + 387 \, x + 32}{162 \, {\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.10, size = 28, normalized size = 0.82 \begin {gather*} \frac {10}{27\,\left (3\,x+2\right )}-\frac {37}{54\,{\left (3\,x+2\right )}^2}+\frac {7}{81\,{\left (3\,x+2\right )}^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 27, normalized size = 0.79 \begin {gather*} - \frac {- 540 x^{2} - 387 x - 32}{4374 x^{3} + 8748 x^{2} + 5832 x + 1296} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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