Optimal. Leaf size=55 \[ \frac {(1-2 x)^4}{126 (2+3 x)^6}-\frac {103 (1-2 x)^4}{2205 (2+3 x)^5}-\frac {103 (1-2 x)^4}{30870 (2+3 x)^4} \]
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Rubi [A]
time = 0.01, antiderivative size = 55, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {79, 47, 37}
\begin {gather*} -\frac {103 (1-2 x)^4}{30870 (3 x+2)^4}-\frac {103 (1-2 x)^4}{2205 (3 x+2)^5}+\frac {(1-2 x)^4}{126 (3 x+2)^6} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rule 47
Rule 79
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (3+5 x)}{(2+3 x)^7} \, dx &=\frac {(1-2 x)^4}{126 (2+3 x)^6}+\frac {103}{63} \int \frac {(1-2 x)^3}{(2+3 x)^6} \, dx\\ &=\frac {(1-2 x)^4}{126 (2+3 x)^6}-\frac {103 (1-2 x)^4}{2205 (2+3 x)^5}+\frac {206 \int \frac {(1-2 x)^3}{(2+3 x)^5} \, dx}{2205}\\ &=\frac {(1-2 x)^4}{126 (2+3 x)^6}-\frac {103 (1-2 x)^4}{2205 (2+3 x)^5}-\frac {103 (1-2 x)^4}{30870 (2+3 x)^4}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 31, normalized size = 0.56 \begin {gather*} \frac {-413+7218 x+3375 x^2+14040 x^3+48600 x^4}{7290 (2+3 x)^6} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 47, normalized size = 0.85
method | result | size |
gosper | \(\frac {48600 x^{4}+14040 x^{3}+3375 x^{2}+7218 x -413}{7290 \left (2+3 x \right )^{6}}\) | \(30\) |
risch | \(\frac {\frac {20}{3} x^{4}+\frac {52}{27} x^{3}+\frac {25}{54} x^{2}+\frac {401}{405} x -\frac {413}{7290}}{\left (2+3 x \right )^{6}}\) | \(30\) |
norman | \(\frac {\frac {351}{32} x^{4}+\frac {3}{2} x +\frac {23}{4} x^{3}+\frac {19}{8} x^{2}+\frac {413}{160} x^{5}+\frac {413}{640} x^{6}}{\left (2+3 x \right )^{6}}\) | \(38\) |
default | \(\frac {20}{243 \left (2+3 x \right )^{2}}-\frac {428}{729 \left (2+3 x \right )^{3}}-\frac {2009}{1215 \left (2+3 x \right )^{5}}+\frac {343}{1458 \left (2+3 x \right )^{6}}+\frac {259}{162 \left (2+3 x \right )^{4}}\) | \(47\) |
meijerg | \(\frac {x \left (\frac {243}{32} x^{5}+\frac {243}{8} x^{4}+\frac {405}{8} x^{3}+45 x^{2}+\frac {45}{2} x +6\right )}{256 \left (1+\frac {3 x}{2}\right )^{6}}-\frac {13 x^{2} \left (\frac {81}{16} x^{4}+\frac {81}{4} x^{3}+\frac {135}{4} x^{2}+30 x +15\right )}{3840 \left (1+\frac {3 x}{2}\right )^{6}}+\frac {x^{3} \left (\frac {27}{8} x^{3}+\frac {27}{2} x^{2}+\frac {45}{2} x +20\right )}{1280 \left (1+\frac {3 x}{2}\right )^{6}}+\frac {3 x^{4} \left (\frac {9}{4} x^{2}+9 x +15\right )}{640 \left (1+\frac {3 x}{2}\right )^{6}}-\frac {x^{5} \left (\frac {3 x}{2}+6\right )}{96 \left (1+\frac {3 x}{2}\right )^{6}}\) | \(135\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 54, normalized size = 0.98 \begin {gather*} \frac {48600 \, x^{4} + 14040 \, x^{3} + 3375 \, x^{2} + 7218 \, x - 413}{7290 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 54, normalized size = 0.98 \begin {gather*} \frac {48600 \, x^{4} + 14040 \, x^{3} + 3375 \, x^{2} + 7218 \, x - 413}{7290 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.16, size = 51, normalized size = 0.93 \begin {gather*} - \frac {- 48600 x^{4} - 14040 x^{3} - 3375 x^{2} - 7218 x + 413}{5314410 x^{6} + 21257640 x^{5} + 35429400 x^{4} + 31492800 x^{3} + 15746400 x^{2} + 4199040 x + 466560} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.14, size = 29, normalized size = 0.53 \begin {gather*} \frac {48600 \, x^{4} + 14040 \, x^{3} + 3375 \, x^{2} + 7218 \, x - 413}{7290 \, {\left (3 \, x + 2\right )}^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 46, normalized size = 0.84 \begin {gather*} \frac {20}{243\,{\left (3\,x+2\right )}^2}-\frac {428}{729\,{\left (3\,x+2\right )}^3}+\frac {259}{162\,{\left (3\,x+2\right )}^4}-\frac {2009}{1215\,{\left (3\,x+2\right )}^5}+\frac {343}{1458\,{\left (3\,x+2\right )}^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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