Optimal. Leaf size=45 \[ -\frac {1}{81 (2+3 x)^7}+\frac {4}{27 (2+3 x)^6}-\frac {13}{27 (2+3 x)^5}+\frac {25}{162 (2+3 x)^4} \]
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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 {25}{162 (3 x+2)^4}-\frac {13}{27 (3 x+2)^5}+\frac {4}{27 (3 x+2)^6}-\frac {1}{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) (3+5 x)^2}{(2+3 x)^8} \, dx &=\int \left (\frac {7}{27 (2+3 x)^8}-\frac {8}{3 (2+3 x)^7}+\frac {65}{9 (2+3 x)^6}-\frac {50}{27 (2+3 x)^5}\right ) \, dx\\ &=-\frac {1}{81 (2+3 x)^7}+\frac {4}{27 (2+3 x)^6}-\frac {13}{27 (2+3 x)^5}+\frac {25}{162 (2+3 x)^4}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 26, normalized size = 0.58 \begin {gather*} \frac {-22+12 x+216 x^2+225 x^3}{54 (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 | \(\frac {225 x^{3}+216 x^{2}+12 x -22}{54 \left (2+3 x \right )^{7}}\) | \(25\) |
risch | \(\frac {\frac {25}{6} x^{3}+4 x^{2}+\frac {2}{9} x -\frac {11}{27}}{\left (2+3 x \right )^{7}}\) | \(25\) |
default | \(-\frac {1}{81 \left (2+3 x \right )^{7}}+\frac {4}{27 \left (2+3 x \right )^{6}}-\frac {13}{27 \left (2+3 x \right )^{5}}+\frac {25}{162 \left (2+3 x \right )^{4}}\) | \(38\) |
norman | \(\frac {\frac {9}{2} x +\frac {93}{4} x^{2}+\frac {1255}{24} x^{3}+\frac {891}{128} x^{7}+\frac {1155}{16} x^{4}+\frac {2079}{32} x^{5}+\frac {2079}{64} x^{6}}{\left (2+3 x \right )^{7}}\) | \(43\) |
meijerg | \(\frac {9 x \left (\frac {729}{64} x^{6}+\frac {1701}{32} x^{5}+\frac {1701}{16} x^{4}+\frac {945}{8} x^{3}+\frac {315}{4} x^{2}+\frac {63}{2} x +7\right )}{1792 \left (1+\frac {3 x}{2}\right )^{7}}+\frac {x^{2} \left (\frac {243}{32} x^{5}+\frac {567}{16} x^{4}+\frac {567}{8} x^{3}+\frac {315}{4} x^{2}+\frac {105}{2} x +21\right )}{896 \left (1+\frac {3 x}{2}\right )^{7}}-\frac {x^{3} \left (\frac {81}{16} x^{4}+\frac {189}{8} x^{3}+\frac {189}{4} x^{2}+\frac {105}{2} x +35\right )}{768 \left (1+\frac {3 x}{2}\right )^{7}}-\frac {5 x^{4} \left (\frac {27}{8} x^{3}+\frac {63}{4} x^{2}+\frac {63}{2} x +35\right )}{3584 \left (1+\frac {3 x}{2}\right )^{7}}\) | \(138\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 54, normalized size = 1.20 \begin {gather*} \frac {225 \, x^{3} + 216 \, x^{2} + 12 \, x - 22}{54 \, {\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 = 0.64, size = 54, normalized size = 1.20 \begin {gather*} \frac {225 \, x^{3} + 216 \, x^{2} + 12 \, x - 22}{54 \, {\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 = 51, normalized size = 1.13 \begin {gather*} - \frac {- 225 x^{3} - 216 x^{2} - 12 x + 22}{118098 x^{7} + 551124 x^{6} + 1102248 x^{5} + 1224720 x^{4} + 816480 x^{3} + 326592 x^{2} + 72576 x + 6912} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.45, size = 24, normalized size = 0.53 \begin {gather*} \frac {225 \, x^{3} + 216 \, x^{2} + 12 \, x - 22}{54 \, {\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 {25}{162\,{\left (3\,x+2\right )}^4}-\frac {13}{27\,{\left (3\,x+2\right )}^5}+\frac {4}{27\,{\left (3\,x+2\right )}^6}-\frac {1}{81\,{\left (3\,x+2\right )}^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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