Optimal. Leaf size=55 \[ -\frac {49}{972 (2+3 x)^4}+\frac {518}{729 (2+3 x)^3}-\frac {503}{162 (2+3 x)^2}+\frac {740}{243 (2+3 x)}+\frac {100}{243} \log (2+3 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 55, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90}
\begin {gather*} \frac {740}{243 (3 x+2)}-\frac {503}{162 (3 x+2)^2}+\frac {518}{729 (3 x+2)^3}-\frac {49}{972 (3 x+2)^4}+\frac {100}{243} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (3+5 x)^2}{(2+3 x)^5} \, dx &=\int \left (\frac {49}{81 (2+3 x)^5}-\frac {518}{81 (2+3 x)^4}+\frac {503}{27 (2+3 x)^3}-\frac {740}{81 (2+3 x)^2}+\frac {100}{81 (2+3 x)}\right ) \, dx\\ &=-\frac {49}{972 (2+3 x)^4}+\frac {518}{729 (2+3 x)^3}-\frac {503}{162 (2+3 x)^2}+\frac {740}{243 (2+3 x)}+\frac {100}{243} \log (2+3 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 41, normalized size = 0.75 \begin {gather*} \frac {38821+217248 x+398034 x^2+239760 x^3+1200 (2+3 x)^4 \log (2+3 x)}{2916 (2+3 x)^4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 46, normalized size = 0.84
method | result | size |
risch | \(\frac {\frac {740}{9} x^{3}+\frac {273}{2} x^{2}+\frac {18104}{243} x +\frac {38821}{2916}}{\left (2+3 x \right )^{4}}+\frac {100 \ln \left (2+3 x \right )}{243}\) | \(34\) |
norman | \(\frac {-\frac {21061}{216} x^{3}-\frac {9337}{216} x^{2}-\frac {871}{162} x -\frac {38821}{576} x^{4}}{\left (2+3 x \right )^{4}}+\frac {100 \ln \left (2+3 x \right )}{243}\) | \(37\) |
default | \(-\frac {49}{972 \left (2+3 x \right )^{4}}+\frac {518}{729 \left (2+3 x \right )^{3}}-\frac {503}{162 \left (2+3 x \right )^{2}}+\frac {740}{243 \left (2+3 x \right )}+\frac {100 \ln \left (2+3 x \right )}{243}\) | \(46\) |
meijerg | \(\frac {9 x \left (\frac {27}{8} x^{3}+9 x^{2}+9 x +4\right )}{128 \left (1+\frac {3 x}{2}\right )^{4}}-\frac {x^{2} \left (\frac {9}{4} x^{2}+6 x +6\right )}{64 \left (1+\frac {3 x}{2}\right )^{4}}-\frac {59 x^{3} \left (\frac {3 x}{2}+4\right )}{384 \left (1+\frac {3 x}{2}\right )^{4}}+\frac {5 x^{4}}{32 \left (1+\frac {3 x}{2}\right )^{4}}-\frac {5 x \left (\frac {3375}{8} x^{3}+585 x^{2}+315 x +60\right )}{486 \left (1+\frac {3 x}{2}\right )^{4}}+\frac {100 \ln \left (1+\frac {3 x}{2}\right )}{243}\) | \(111\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 48, normalized size = 0.87 \begin {gather*} \frac {239760 \, x^{3} + 398034 \, x^{2} + 217248 \, x + 38821}{2916 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac {100}{243} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.44, size = 67, normalized size = 1.22 \begin {gather*} \frac {239760 \, x^{3} + 398034 \, x^{2} + 1200 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 217248 \, x + 38821}{2916 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 44, normalized size = 0.80 \begin {gather*} \frac {239760 x^{3} + 398034 x^{2} + 217248 x + 38821}{236196 x^{4} + 629856 x^{3} + 629856 x^{2} + 279936 x + 46656} + \frac {100 \log {\left (3 x + 2 \right )}}{243} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.30, size = 55, normalized size = 1.00 \begin {gather*} \frac {740}{243 \, {\left (3 \, x + 2\right )}} - \frac {503}{162 \, {\left (3 \, x + 2\right )}^{2}} + \frac {518}{729 \, {\left (3 \, x + 2\right )}^{3}} - \frac {49}{972 \, {\left (3 \, x + 2\right )}^{4}} - \frac {100}{243} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 43, normalized size = 0.78 \begin {gather*} \frac {100\,\ln \left (x+\frac {2}{3}\right )}{243}+\frac {\frac {740\,x^3}{729}+\frac {91\,x^2}{54}+\frac {18104\,x}{19683}+\frac {38821}{236196}}{x^4+\frac {8\,x^3}{3}+\frac {8\,x^2}{3}+\frac {32\,x}{27}+\frac {16}{81}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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