Optimal. Leaf size=52 \[ -\frac {54 x^3}{125}-\frac {297 x^2}{1250}+\frac {1647 x}{3125}-\frac {26}{3125 (5 x+3)}-\frac {11}{31250 (5 x+3)^2}+\frac {114 \log (5 x+3)}{3125} \]
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Rubi [A] time = 0.02, antiderivative size = 52, 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 {54 x^3}{125}-\frac {297 x^2}{1250}+\frac {1647 x}{3125}-\frac {26}{3125 (5 x+3)}-\frac {11}{31250 (5 x+3)^2}+\frac {114 \log (5 x+3)}{3125} \end {gather*}
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)^3} \, dx &=\int \left (\frac {1647}{3125}-\frac {297 x}{625}-\frac {162 x^2}{125}+\frac {11}{3125 (3+5 x)^3}+\frac {26}{625 (3+5 x)^2}+\frac {114}{625 (3+5 x)}\right ) \, dx\\ &=\frac {1647 x}{3125}-\frac {297 x^2}{1250}-\frac {54 x^3}{125}-\frac {11}{31250 (3+5 x)^2}-\frac {26}{3125 (3+5 x)}+\frac {114 \log (3+5 x)}{3125}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 51, normalized size = 0.98 \begin {gather*} \frac {-67500 x^5-118125 x^4+13500 x^3+133650 x^2+87220 x+228 (5 x+3)^2 \log (5 x+3)+17192}{6250 (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)^4}{(3+5 x)^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.29, size = 57, normalized size = 1.10 \begin {gather*} -\frac {337500 \, x^{5} + 590625 \, x^{4} - 67500 \, x^{3} - 427275 \, x^{2} - 1140 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 146930 \, x + 791}{31250 \, {\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 = 1.31, size = 37, normalized size = 0.71 \begin {gather*} -\frac {54}{125} \, x^{3} - \frac {297}{1250} \, x^{2} + \frac {1647}{3125} \, x - \frac {1300 \, x + 791}{31250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {114}{3125} \, \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 = 41, normalized size = 0.79 \begin {gather*} -\frac {54 x^{3}}{125}-\frac {297 x^{2}}{1250}+\frac {1647 x}{3125}+\frac {114 \ln \left (5 x +3\right )}{3125}-\frac {11}{31250 \left (5 x +3\right )^{2}}-\frac {26}{3125 \left (5 x +3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.67, size = 41, normalized size = 0.79 \begin {gather*} -\frac {54}{125} \, x^{3} - \frac {297}{1250} \, x^{2} + \frac {1647}{3125} \, x - \frac {1300 \, x + 791}{31250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {114}{3125} \, \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 = 0.03, size = 37, normalized size = 0.71 \begin {gather*} \frac {1647\,x}{3125}+\frac {114\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {\frac {26\,x}{15625}+\frac {791}{781250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}-\frac {297\,x^2}{1250}-\frac {54\,x^3}{125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 42, normalized size = 0.81 \begin {gather*} - \frac {54 x^{3}}{125} - \frac {297 x^{2}}{1250} + \frac {1647 x}{3125} - \frac {1300 x + 791}{781250 x^{2} + 937500 x + 281250} + \frac {114 \log {\left (5 x + 3 \right )}}{3125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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