Optimal. Leaf size=45 \[ -\frac {10}{81 (3 x+2)^2}+\frac {16}{27 (3 x+2)^3}-\frac {91}{108 (3 x+2)^4}+\frac {49}{405 (3 x+2)^5} \]
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Rubi [A] time = 0.02, antiderivative size = 45, 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 {10}{81 (3 x+2)^2}+\frac {16}{27 (3 x+2)^3}-\frac {91}{108 (3 x+2)^4}+\frac {49}{405 (3 x+2)^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^6} \, dx &=\int \left (-\frac {49}{27 (2+3 x)^6}+\frac {91}{9 (2+3 x)^5}-\frac {16}{3 (2+3 x)^4}+\frac {20}{27 (2+3 x)^3}\right ) \, dx\\ &=\frac {49}{405 (2+3 x)^5}-\frac {91}{108 (2+3 x)^4}+\frac {16}{27 (2+3 x)^3}-\frac {10}{81 (2+3 x)^2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 26, normalized size = 0.58 \begin {gather*} -\frac {1800 x^3+720 x^2-75 x+98}{540 (3 x+2)^5} \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)^2 (3+5 x)}{(2+3 x)^6} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.33, size = 44, normalized size = 0.98 \begin {gather*} -\frac {1800 \, x^{3} + 720 \, x^{2} - 75 \, x + 98}{540 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.20, size = 24, normalized size = 0.53 \begin {gather*} -\frac {1800 \, x^{3} + 720 \, x^{2} - 75 \, x + 98}{540 \, {\left (3 \, x + 2\right )}^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 38, normalized size = 0.84 \begin {gather*} \frac {49}{405 \left (3 x +2\right )^{5}}-\frac {91}{108 \left (3 x +2\right )^{4}}+\frac {16}{27 \left (3 x +2\right )^{3}}-\frac {10}{81 \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 = 0.59, size = 44, normalized size = 0.98 \begin {gather*} -\frac {1800 \, x^{3} + 720 \, x^{2} - 75 \, x + 98}{540 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.10, size = 37, normalized size = 0.82 \begin {gather*} \frac {16}{27\,{\left (3\,x+2\right )}^3}-\frac {10}{81\,{\left (3\,x+2\right )}^2}-\frac {91}{108\,{\left (3\,x+2\right )}^4}+\frac {49}{405\,{\left (3\,x+2\right )}^5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 39, normalized size = 0.87 \begin {gather*} \frac {- 1800 x^{3} - 720 x^{2} + 75 x - 98}{131220 x^{5} + 437400 x^{4} + 583200 x^{3} + 388800 x^{2} + 129600 x + 17280} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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