Optimal. Leaf size=30 \[ -\frac {6 x^3}{5}-\frac {21 x^2}{50}+\frac {163 x}{125}+\frac {11}{625} \log (5 x+3) \]
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Rubi [A] time = 0.01, antiderivative size = 30, 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 = {77} \[ -\frac {6 x^3}{5}-\frac {21 x^2}{50}+\frac {163 x}{125}+\frac {11}{625} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)^2}{3+5 x} \, dx &=\int \left (\frac {163}{125}-\frac {21 x}{25}-\frac {18 x^2}{5}+\frac {11}{125 (3+5 x)}\right ) \, dx\\ &=\frac {163 x}{125}-\frac {21 x^2}{50}-\frac {6 x^3}{5}+\frac {11}{625} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 27, normalized size = 0.90 \[ \frac {-1500 x^3-525 x^2+1630 x+22 \log (5 x+3)+843}{1250} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 22, normalized size = 0.73 \[ -\frac {6}{5} \, x^{3} - \frac {21}{50} \, x^{2} + \frac {163}{125} \, x + \frac {11}{625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.16, size = 23, normalized size = 0.77 \[ -\frac {6}{5} \, x^{3} - \frac {21}{50} \, x^{2} + \frac {163}{125} \, x + \frac {11}{625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 23, normalized size = 0.77 \[ -\frac {6 x^{3}}{5}-\frac {21 x^{2}}{50}+\frac {163 x}{125}+\frac {11 \ln \left (5 x +3\right )}{625} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 22, normalized size = 0.73 \[ -\frac {6}{5} \, x^{3} - \frac {21}{50} \, x^{2} + \frac {163}{125} \, x + \frac {11}{625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 20, normalized size = 0.67 \[ \frac {163\,x}{125}+\frac {11\,\ln \left (x+\frac {3}{5}\right )}{625}-\frac {21\,x^2}{50}-\frac {6\,x^3}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 27, normalized size = 0.90 \[ - \frac {6 x^{3}}{5} - \frac {21 x^{2}}{50} + \frac {163 x}{125} + \frac {11 \log {\left (5 x + 3 \right )}}{625} \]
Verification of antiderivative is not currently implemented for this CAS.
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