Optimal. Leaf size=41 \[ \frac {12 x^3}{25}-\frac {78 x^2}{125}+\frac {37 x}{625}-\frac {121}{3125 (5 x+3)}+\frac {682 \log (5 x+3)}{3125} \]
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Rubi [A] time = 0.02, antiderivative size = 41, 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 = {88} \[ \frac {12 x^3}{25}-\frac {78 x^2}{125}+\frac {37 x}{625}-\frac {121}{3125 (5 x+3)}+\frac {682 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (2+3 x)^2}{(3+5 x)^2} \, dx &=\int \left (\frac {37}{625}-\frac {156 x}{125}+\frac {36 x^2}{25}+\frac {121}{625 (3+5 x)^2}+\frac {682}{625 (3+5 x)}\right ) \, dx\\ &=\frac {37 x}{625}-\frac {78 x^2}{125}+\frac {12 x^3}{25}-\frac {121}{3125 (3+5 x)}+\frac {682 \log (3+5 x)}{3125}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 42, normalized size = 1.02 \[ \frac {\frac {5 \left (1500 x^4-1050 x^3-985 x^2+1248 x+658\right )}{5 x+3}+682 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 42, normalized size = 1.02 \[ \frac {7500 \, x^{4} - 5250 \, x^{3} - 4925 \, x^{2} + 682 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 555 \, x - 121}{3125 \, {\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 57, normalized size = 1.39 \[ -\frac {1}{3125} \, {\left (5 \, x + 3\right )}^{3} {\left (\frac {186}{5 \, x + 3} - \frac {829}{{\left (5 \, x + 3\right )}^{2}} - 12\right )} - \frac {121}{3125 \, {\left (5 \, x + 3\right )}} - \frac {682}{3125} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 32, normalized size = 0.78 \[ \frac {12 x^{3}}{25}-\frac {78 x^{2}}{125}+\frac {37 x}{625}+\frac {682 \ln \left (5 x +3\right )}{3125}-\frac {121}{3125 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.62, size = 31, normalized size = 0.76 \[ \frac {12}{25} \, x^{3} - \frac {78}{125} \, x^{2} + \frac {37}{625} \, x - \frac {121}{3125 \, {\left (5 \, x + 3\right )}} + \frac {682}{3125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 29, normalized size = 0.71 \[ \frac {37\,x}{625}+\frac {682\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {121}{15625\,\left (x+\frac {3}{5}\right )}-\frac {78\,x^2}{125}+\frac {12\,x^3}{25} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 34, normalized size = 0.83 \[ \frac {12 x^{3}}{25} - \frac {78 x^{2}}{125} + \frac {37 x}{625} + \frac {682 \log {\left (5 x + 3 \right )}}{3125} - \frac {121}{15625 x + 9375} \]
Verification of antiderivative is not currently implemented for this CAS.
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