Optimal. Leaf size=59 \[ -\frac{243 x^4}{250}-\frac{837 x^3}{625}+\frac{1971 x^2}{6250}+\frac{3636 x}{3125}-\frac{163}{78125 (5 x+3)}-\frac{11}{156250 (5 x+3)^2}+\frac{192 \log (5 x+3)}{15625} \]
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Rubi [A] time = 0.0268993, antiderivative size = 59, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{243 x^4}{250}-\frac{837 x^3}{625}+\frac{1971 x^2}{6250}+\frac{3636 x}{3125}-\frac{163}{78125 (5 x+3)}-\frac{11}{156250 (5 x+3)^2}+\frac{192 \log (5 x+3)}{15625} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (2+3 x)^5}{(3+5 x)^3} \, dx &=\int \left (\frac{3636}{3125}+\frac{1971 x}{3125}-\frac{2511 x^2}{625}-\frac{486 x^3}{125}+\frac{11}{15625 (3+5 x)^3}+\frac{163}{15625 (3+5 x)^2}+\frac{192}{3125 (3+5 x)}\right ) \, dx\\ &=\frac{3636 x}{3125}+\frac{1971 x^2}{6250}-\frac{837 x^3}{625}-\frac{243 x^4}{250}-\frac{11}{156250 (3+5 x)^2}-\frac{163}{78125 (3+5 x)}+\frac{192 \log (3+5 x)}{15625}\\ \end{align*}
Mathematica [A] time = 0.0165377, size = 58, normalized size = 0.98 \[ \frac{-3796875 x^6-9787500 x^5-6412500 x^4+4140000 x^3+7579975 x^2+3653570 x+1920 (5 x+3)^2 \log (-3 (5 x+3))+604711}{156250 (5 x+3)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 46, normalized size = 0.8 \begin{align*}{\frac{3636\,x}{3125}}+{\frac{1971\,{x}^{2}}{6250}}-{\frac{837\,{x}^{3}}{625}}-{\frac{243\,{x}^{4}}{250}}-{\frac{11}{156250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{163}{234375+390625\,x}}+{\frac{192\,\ln \left ( 3+5\,x \right ) }{15625}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.17465, size = 62, normalized size = 1.05 \begin{align*} -\frac{243}{250} \, x^{4} - \frac{837}{625} \, x^{3} + \frac{1971}{6250} \, x^{2} + \frac{3636}{3125} \, x - \frac{1630 \, x + 989}{156250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{192}{15625} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.54839, size = 215, normalized size = 3.64 \begin{align*} -\frac{3796875 \, x^{6} + 9787500 \, x^{5} + 6412500 \, x^{4} - 4140000 \, x^{3} - 5897475 \, x^{2} - 1920 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 1634570 \, x + 989}{156250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.121336, size = 49, normalized size = 0.83 \begin{align*} - \frac{243 x^{4}}{250} - \frac{837 x^{3}}{625} + \frac{1971 x^{2}}{6250} + \frac{3636 x}{3125} - \frac{1630 x + 989}{3906250 x^{2} + 4687500 x + 1406250} + \frac{192 \log{\left (5 x + 3 \right )}}{15625} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.36902, size = 57, normalized size = 0.97 \begin{align*} -\frac{243}{250} \, x^{4} - \frac{837}{625} \, x^{3} + \frac{1971}{6250} \, x^{2} + \frac{3636}{3125} \, x - \frac{1630 \, x + 989}{156250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{192}{15625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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