Optimal. Leaf size=34 \[ \frac {5}{27 (3 x+2)^2}-\frac {37}{81 (3 x+2)^3}+\frac {7}{108 (3 x+2)^4} \]
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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 {5}{27 (3 x+2)^2}-\frac {37}{81 (3 x+2)^3}+\frac {7}{108 (3 x+2)^4} \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)^5} \, dx &=\int \left (-\frac {7}{9 (2+3 x)^5}+\frac {37}{9 (2+3 x)^4}-\frac {10}{9 (2+3 x)^3}\right ) \, dx\\ &=\frac {7}{108 (2+3 x)^4}-\frac {37}{81 (2+3 x)^3}+\frac {5}{27 (2+3 x)^2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 0.62 \begin {gather*} \frac {540 x^2+276 x-35}{324 (3 x+2)^4} \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)^5} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.11, size = 34, normalized size = 1.00 \begin {gather*} \frac {540 \, x^{2} + 276 \, x - 35}{324 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.17, size = 28, normalized size = 0.82 \begin {gather*} \frac {5}{27 \, {\left (3 \, x + 2\right )}^{2}} - \frac {37}{81 \, {\left (3 \, x + 2\right )}^{3}} + \frac {7}{108 \, {\left (3 \, x + 2\right )}^{4}} \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}{108 \left (3 x +2\right )^{4}}-\frac {37}{81 \left (3 x +2\right )^{3}}+\frac {5}{27 \left (3 x +2\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 34, normalized size = 1.00 \begin {gather*} \frac {540 \, x^{2} + 276 \, x - 35}{324 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.11, size = 28, normalized size = 0.82 \begin {gather*} \frac {5}{27\,{\left (3\,x+2\right )}^2}-\frac {37}{81\,{\left (3\,x+2\right )}^3}+\frac {7}{108\,{\left (3\,x+2\right )}^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 31, normalized size = 0.91 \begin {gather*} - \frac {- 540 x^{2} - 276 x + 35}{26244 x^{4} + 69984 x^{3} + 69984 x^{2} + 31104 x + 5184} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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