Optimal. Leaf size=45 \[ \frac {7}{81 (2+3 x)^7}-\frac {91}{162 (2+3 x)^6}+\frac {16}{45 (2+3 x)^5}-\frac {5}{81 (2+3 x)^4} \]
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Rubi [A]
time = 0.01, 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 = {78}
\begin {gather*} -\frac {5}{81 (3 x+2)^4}+\frac {16}{45 (3 x+2)^5}-\frac {91}{162 (3 x+2)^6}+\frac {7}{81 (3 x+2)^7} \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^8} \, dx &=\int \left (-\frac {49}{27 (2+3 x)^8}+\frac {91}{9 (2+3 x)^7}-\frac {16}{3 (2+3 x)^6}+\frac {20}{27 (2+3 x)^5}\right ) \, dx\\ &=\frac {7}{81 (2+3 x)^7}-\frac {91}{162 (2+3 x)^6}+\frac {16}{45 (2+3 x)^5}-\frac {5}{81 (2+3 x)^4}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 26, normalized size = 0.58 \begin {gather*} -\frac {88-291 x+108 x^2+1350 x^3}{810 (2+3 x)^7} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 38, normalized size = 0.84
method | result | size |
gosper | \(-\frac {1350 x^{3}+108 x^{2}-291 x +88}{810 \left (2+3 x \right )^{7}}\) | \(25\) |
risch | \(\frac {-\frac {5}{3} x^{3}-\frac {2}{15} x^{2}+\frac {97}{270} x -\frac {44}{405}}{\left (2+3 x \right )^{7}}\) | \(25\) |
default | \(\frac {7}{81 \left (2+3 x \right )^{7}}-\frac {91}{162 \left (2+3 x \right )^{6}}+\frac {16}{45 \left (2+3 x \right )^{5}}-\frac {5}{81 \left (2+3 x \right )^{4}}\) | \(38\) |
norman | \(\frac {\frac {67}{6} x^{3}+\frac {3}{2} x +5 x^{2}+\frac {297}{160} x^{7}+\frac {77}{4} x^{4}+\frac {693}{40} x^{5}+\frac {693}{80} x^{6}}{\left (2+3 x \right )^{7}}\) | \(43\) |
meijerg | \(\frac {3 x \left (\frac {729}{64} x^{6}+\frac {1701}{32} x^{5}+\frac {1701}{16} x^{4}+\frac {945}{8} x^{3}+\frac {315}{4} x^{2}+\frac {63}{2} x +7\right )}{1792 \left (1+\frac {3 x}{2}\right )^{7}}-\frac {x^{2} \left (\frac {243}{32} x^{5}+\frac {567}{16} x^{4}+\frac {567}{8} x^{3}+\frac {315}{4} x^{2}+\frac {105}{2} x +21\right )}{1536 \left (1+\frac {3 x}{2}\right )^{7}}-\frac {x^{3} \left (\frac {81}{16} x^{4}+\frac {189}{8} x^{3}+\frac {189}{4} x^{2}+\frac {105}{2} x +35\right )}{3360 \left (1+\frac {3 x}{2}\right )^{7}}+\frac {x^{4} \left (\frac {27}{8} x^{3}+\frac {63}{4} x^{2}+\frac {63}{2} x +35\right )}{1792 \left (1+\frac {3 x}{2}\right )^{7}}\) | \(138\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 54, normalized size = 1.20 \begin {gather*} -\frac {1350 \, x^{3} + 108 \, x^{2} - 291 \, x + 88}{810 \, {\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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Fricas [A]
time = 0.44, size = 54, normalized size = 1.20 \begin {gather*} -\frac {1350 \, x^{3} + 108 \, x^{2} - 291 \, x + 88}{810 \, {\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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Sympy [A]
time = 0.07, size = 49, normalized size = 1.09 \begin {gather*} \frac {- 1350 x^{3} - 108 x^{2} + 291 x - 88}{1771470 x^{7} + 8266860 x^{6} + 16533720 x^{5} + 18370800 x^{4} + 12247200 x^{3} + 4898880 x^{2} + 1088640 x + 103680} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.69, size = 24, normalized size = 0.53 \begin {gather*} -\frac {1350 \, x^{3} + 108 \, x^{2} - 291 \, x + 88}{810 \, {\left (3 \, x + 2\right )}^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.11, size = 37, normalized size = 0.82 \begin {gather*} \frac {16}{45\,{\left (3\,x+2\right )}^5}-\frac {5}{81\,{\left (3\,x+2\right )}^4}-\frac {91}{162\,{\left (3\,x+2\right )}^6}+\frac {7}{81\,{\left (3\,x+2\right )}^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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