Optimal. Leaf size=34 \[ -\frac {9 x^2}{25}+\frac {33 x}{125}-\frac {11}{625 (5 x+3)}+\frac {64}{625} \log (5 x+3) \]
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Rubi [A] time = 0.01, antiderivative size = 34, 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} \[ -\frac {9 x^2}{25}+\frac {33 x}{125}-\frac {11}{625 (5 x+3)}+\frac {64}{625} \log (5 x+3) \]
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)^2} \, dx &=\int \left (\frac {33}{125}-\frac {18 x}{25}+\frac {11}{125 (3+5 x)^2}+\frac {64}{125 (3+5 x)}\right ) \, dx\\ &=\frac {33 x}{125}-\frac {9 x^2}{25}-\frac {11}{625 (3+5 x)}+\frac {64}{625} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 41, normalized size = 1.21 \[ \frac {-1125 x^3+150 x^2+1545 x+64 (5 x+3) \log (-3 (5 x+3))+619}{625 (5 x+3)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 37, normalized size = 1.09 \[ -\frac {1125 \, x^{3} - 150 \, x^{2} - 64 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 495 \, x + 11}{625 \, {\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.17, size = 48, normalized size = 1.41 \[ \frac {3}{625} \, {\left (5 \, x + 3\right )}^{2} {\left (\frac {29}{5 \, x + 3} - 3\right )} - \frac {11}{625 \, {\left (5 \, x + 3\right )}} - \frac {64}{625} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 27, normalized size = 0.79 \[ -\frac {9 x^{2}}{25}+\frac {33 x}{125}+\frac {64 \ln \left (5 x +3\right )}{625}-\frac {11}{625 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 26, normalized size = 0.76 \[ -\frac {9}{25} \, x^{2} + \frac {33}{125} \, x - \frac {11}{625 \, {\left (5 \, x + 3\right )}} + \frac {64}{625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 24, normalized size = 0.71 \[ \frac {33\,x}{125}+\frac {64\,\ln \left (x+\frac {3}{5}\right )}{625}-\frac {11}{3125\,\left (x+\frac {3}{5}\right )}-\frac {9\,x^2}{25} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 27, normalized size = 0.79 \[ - \frac {9 x^{2}}{25} + \frac {33 x}{125} + \frac {64 \log {\left (5 x + 3 \right )}}{625} - \frac {11}{3125 x + 1875} \]
Verification of antiderivative is not currently implemented for this CAS.
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