Optimal. Leaf size=33 \[ -\frac {31}{125 (5 x+3)}-\frac {11}{250 (5 x+3)^2}-\frac {6}{125} \log (5 x+3) \]
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Rubi [A] time = 0.01, antiderivative size = 33, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {77} \[ -\frac {31}{125 (5 x+3)}-\frac {11}{250 (5 x+3)^2}-\frac {6}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)}{(3+5 x)^3} \, dx &=\int \left (\frac {11}{25 (3+5 x)^3}+\frac {31}{25 (3+5 x)^2}-\frac {6}{25 (3+5 x)}\right ) \, dx\\ &=-\frac {11}{250 (3+5 x)^2}-\frac {31}{125 (3+5 x)}-\frac {6}{125} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.01, size = 33, normalized size = 1.00 \[ -\frac {31}{125 (5 x+3)}-\frac {11}{250 (5 x+3)^2}-\frac {6}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
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fricas [A] time = 1.12, size = 37, normalized size = 1.12 \[ -\frac {12 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 310 \, x + 197}{250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.24, size = 24, normalized size = 0.73 \[ -\frac {310 \, x + 197}{250 \, {\left (5 \, x + 3\right )}^{2}} - \frac {6}{125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 28, normalized size = 0.85 \[ -\frac {6 \ln \left (5 x +3\right )}{125}-\frac {11}{250 \left (5 x +3\right )^{2}}-\frac {31}{125 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.66, size = 28, normalized size = 0.85 \[ -\frac {310 \, x + 197}{250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} - \frac {6}{125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.11, size = 24, normalized size = 0.73 \[ -\frac {6\,\ln \left (x+\frac {3}{5}\right )}{125}-\frac {\frac {31\,x}{625}+\frac {197}{6250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 26, normalized size = 0.79 \[ - \frac {310 x + 197}{6250 x^{2} + 7500 x + 2250} - \frac {6 \log {\left (5 x + 3 \right )}}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
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