Optimal. Leaf size=37 \[ \frac {(1-2 x)^4}{105 (3 x+2)^5}-\frac {173 (1-2 x)^4}{2940 (3 x+2)^4} \]
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Rubi [A] time = 0.01, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {78, 37} \[ \frac {(1-2 x)^4}{105 (3 x+2)^5}-\frac {173 (1-2 x)^4}{2940 (3 x+2)^4} \]
Antiderivative was successfully verified.
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Rule 37
Rule 78
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^6} \, dx &=\frac {(1-2 x)^4}{105 (2+3 x)^5}+\frac {173}{105} \int \frac {(1-2 x)^3}{(2+3 x)^5} \, dx\\ &=\frac {(1-2 x)^4}{105 (2+3 x)^5}-\frac {173 (1-2 x)^4}{2940 (2+3 x)^4}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 31, normalized size = 0.84 \[ \frac {64800 x^4+57240 x^3+34920 x^2+16905 x+1282}{4860 (3 x+2)^5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 49, normalized size = 1.32 \[ \frac {64800 \, x^{4} + 57240 \, x^{3} + 34920 \, x^{2} + 16905 \, x + 1282}{4860 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.76, size = 29, normalized size = 0.78 \[ \frac {64800 \, x^{4} + 57240 \, x^{3} + 34920 \, x^{2} + 16905 \, x + 1282}{4860 \, {\left (3 \, x + 2\right )}^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 47, normalized size = 1.27 \[ \frac {518}{243 \left (3 x +2\right )^{3}}-\frac {2009}{972 \left (3 x +2\right )^{4}}-\frac {214}{243 \left (3 x +2\right )^{2}}+\frac {40}{243 \left (3 x +2\right )}+\frac {343}{1215 \left (3 x +2\right )^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 49, normalized size = 1.32 \[ \frac {64800 \, x^{4} + 57240 \, x^{3} + 34920 \, x^{2} + 16905 \, x + 1282}{4860 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 46, normalized size = 1.24 \[ \frac {40}{243\,\left (3\,x+2\right )}-\frac {214}{243\,{\left (3\,x+2\right )}^2}+\frac {518}{243\,{\left (3\,x+2\right )}^3}-\frac {2009}{972\,{\left (3\,x+2\right )}^4}+\frac {343}{1215\,{\left (3\,x+2\right )}^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 48, normalized size = 1.30 \[ - \frac {- 64800 x^{4} - 57240 x^{3} - 34920 x^{2} - 16905 x - 1282}{1180980 x^{5} + 3936600 x^{4} + 5248800 x^{3} + 3499200 x^{2} + 1166400 x + 155520} \]
Verification of antiderivative is not currently implemented for this CAS.
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