Optimal. Leaf size=48 \[ -\frac {81 x^4}{50}-\frac {261 x^3}{125}+\frac {378 x^2}{625}+\frac {5511 x}{3125}-\frac {11}{15625 (5 x+3)}+\frac {26 \log (5 x+3)}{3125} \]
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Rubi [A] time = 0.02, antiderivative size = 48, 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} \[ -\frac {81 x^4}{50}-\frac {261 x^3}{125}+\frac {378 x^2}{625}+\frac {5511 x}{3125}-\frac {11}{15625 (5 x+3)}+\frac {26 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)^4}{(3+5 x)^2} \, dx &=\int \left (\frac {5511}{3125}+\frac {756 x}{625}-\frac {783 x^2}{125}-\frac {162 x^3}{25}+\frac {11}{3125 (3+5 x)^2}+\frac {26}{625 (3+5 x)}\right ) \, dx\\ &=\frac {5511 x}{3125}+\frac {378 x^2}{625}-\frac {261 x^3}{125}-\frac {81 x^4}{50}-\frac {11}{15625 (3+5 x)}+\frac {26 \log (3+5 x)}{3125}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 49, normalized size = 1.02 \[ \frac {-50625 x^5-95625 x^4-20250 x^3+66450 x^2+51795 x+52 (5 x+3) \log (5 x+3)+11233}{6250 (5 x+3)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 47, normalized size = 0.98 \[ -\frac {253125 \, x^{5} + 478125 \, x^{4} + 101250 \, x^{3} - 332250 \, x^{2} - 260 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 165330 \, x + 22}{31250 \, {\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.22, size = 66, normalized size = 1.38 \[ \frac {3}{31250} \, {\left (5 \, x + 3\right )}^{4} {\left (\frac {150}{5 \, x + 3} + \frac {360}{{\left (5 \, x + 3\right )}^{2}} + \frac {380}{{\left (5 \, x + 3\right )}^{3}} - 27\right )} - \frac {11}{15625 \, {\left (5 \, x + 3\right )}} - \frac {26}{3125} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 37, normalized size = 0.77 \[ -\frac {81 x^{4}}{50}-\frac {261 x^{3}}{125}+\frac {378 x^{2}}{625}+\frac {5511 x}{3125}+\frac {26 \ln \left (5 x +3\right )}{3125}-\frac {11}{15625 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 36, normalized size = 0.75 \[ -\frac {81}{50} \, x^{4} - \frac {261}{125} \, x^{3} + \frac {378}{625} \, x^{2} + \frac {5511}{3125} \, x - \frac {11}{15625 \, {\left (5 \, x + 3\right )}} + \frac {26}{3125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 34, normalized size = 0.71 \[ \frac {5511\,x}{3125}+\frac {26\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {11}{78125\,\left (x+\frac {3}{5}\right )}+\frac {378\,x^2}{625}-\frac {261\,x^3}{125}-\frac {81\,x^4}{50} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 41, normalized size = 0.85 \[ - \frac {81 x^{4}}{50} - \frac {261 x^{3}}{125} + \frac {378 x^{2}}{625} + \frac {5511 x}{3125} + \frac {26 \log {\left (5 x + 3 \right )}}{3125} - \frac {11}{78125 x + 46875} \]
Verification of antiderivative is not currently implemented for this CAS.
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