Optimal. Leaf size=37 \[ \frac {793 x}{625}-\frac {431 x^2}{250}-\frac {16 x^3}{25}+\frac {9 x^4}{5}+\frac {121 \log (3+5 x)}{3125} \]
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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 = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90}
\begin {gather*} \frac {9 x^4}{5}-\frac {16 x^3}{25}-\frac {431 x^2}{250}+\frac {793 x}{625}+\frac {121 \log (5 x+3)}{3125} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (2+3 x)^2}{3+5 x} \, dx &=\int \left (\frac {793}{625}-\frac {431 x}{125}-\frac {48 x^2}{25}+\frac {36 x^3}{5}+\frac {121}{625 (3+5 x)}\right ) \, dx\\ &=\frac {793 x}{625}-\frac {431 x^2}{250}-\frac {16 x^3}{25}+\frac {9 x^4}{5}+\frac {121 \log (3+5 x)}{3125}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 35, normalized size = 0.95 \begin {gather*} \frac {5 \left (1263+1586 x-2155 x^2-800 x^3+2250 x^4\right )+242 \log (3+5 x)}{6250} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 28, normalized size = 0.76
method | result | size |
default | \(\frac {793 x}{625}-\frac {431 x^{2}}{250}-\frac {16 x^{3}}{25}+\frac {9 x^{4}}{5}+\frac {121 \ln \left (3+5 x \right )}{3125}\) | \(28\) |
norman | \(\frac {793 x}{625}-\frac {431 x^{2}}{250}-\frac {16 x^{3}}{25}+\frac {9 x^{4}}{5}+\frac {121 \ln \left (3+5 x \right )}{3125}\) | \(28\) |
risch | \(\frac {793 x}{625}-\frac {431 x^{2}}{250}-\frac {16 x^{3}}{25}+\frac {9 x^{4}}{5}+\frac {121 \ln \left (3+5 x \right )}{3125}\) | \(28\) |
meijerg | \(\frac {121 \ln \left (1+\frac {5 x}{3}\right )}{3125}-\frac {4 x}{5}+\frac {23 x \left (-5 x +6\right )}{50}+\frac {9 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{125}-\frac {81 x \left (-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{3125}\) | \(52\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 27, normalized size = 0.73 \begin {gather*} \frac {9}{5} \, x^{4} - \frac {16}{25} \, x^{3} - \frac {431}{250} \, x^{2} + \frac {793}{625} \, x + \frac {121}{3125} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 27, normalized size = 0.73 \begin {gather*} \frac {9}{5} \, x^{4} - \frac {16}{25} \, x^{3} - \frac {431}{250} \, x^{2} + \frac {793}{625} \, x + \frac {121}{3125} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 34, normalized size = 0.92 \begin {gather*} \frac {9 x^{4}}{5} - \frac {16 x^{3}}{25} - \frac {431 x^{2}}{250} + \frac {793 x}{625} + \frac {121 \log {\left (5 x + 3 \right )}}{3125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.77, size = 28, normalized size = 0.76 \begin {gather*} \frac {9}{5} \, x^{4} - \frac {16}{25} \, x^{3} - \frac {431}{250} \, x^{2} + \frac {793}{625} \, x + \frac {121}{3125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 25, normalized size = 0.68 \begin {gather*} \frac {793\,x}{625}+\frac {121\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {431\,x^2}{250}-\frac {16\,x^3}{25}+\frac {9\,x^4}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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