Optimal. Leaf size=38 \[ -\frac {18 x}{125}-\frac {64}{625 (5 x+3)}-\frac {11}{1250 (5 x+3)^2}+\frac {87}{625} \log (5 x+3) \]
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Rubi [A] time = 0.02, antiderivative size = 38, 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} \begin {gather*} -\frac {18 x}{125}-\frac {64}{625 (5 x+3)}-\frac {11}{1250 (5 x+3)^2}+\frac {87}{625} \log (5 x+3) \end {gather*}
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)^3} \, dx &=\int \left (-\frac {18}{125}+\frac {11}{125 (3+5 x)^3}+\frac {64}{125 (3+5 x)^2}+\frac {87}{125 (3+5 x)}\right ) \, dx\\ &=-\frac {18 x}{125}-\frac {11}{1250 (3+5 x)^2}-\frac {64}{625 (3+5 x)}+\frac {87}{625} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 39, normalized size = 1.03 \begin {gather*} \frac {87}{625} \log (-3 (5 x+3))-\frac {900 x^3+1680 x^2+1172 x+295}{250 (5 x+3)^2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1-2 x) (2+3 x)^2}{(3+5 x)^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.27, size = 47, normalized size = 1.24 \begin {gather*} -\frac {4500 \, x^{3} + 5400 \, x^{2} - 174 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 2260 \, x + 395}{1250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.19, size = 27, normalized size = 0.71 \begin {gather*} -\frac {18}{125} \, x - \frac {128 \, x + 79}{250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {87}{625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 31, normalized size = 0.82 \begin {gather*} -\frac {18 x}{125}+\frac {87 \ln \left (5 x +3\right )}{625}-\frac {11}{1250 \left (5 x +3\right )^{2}}-\frac {64}{625 \left (5 x +3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 31, normalized size = 0.82 \begin {gather*} -\frac {18}{125} \, x - \frac {128 \, x + 79}{250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {87}{625} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 27, normalized size = 0.71 \begin {gather*} \frac {87\,\ln \left (x+\frac {3}{5}\right )}{625}-\frac {18\,x}{125}-\frac {\frac {64\,x}{3125}+\frac {79}{6250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 29, normalized size = 0.76 \begin {gather*} - \frac {18 x}{125} - \frac {128 x + 79}{6250 x^{2} + 7500 x + 2250} + \frac {87 \log {\left (5 x + 3 \right )}}{625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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