Optimal. Leaf size=43 \[ \frac {4719}{125 (5 x+3)}-\frac {1331}{250 (5 x+3)^2}-\frac {343}{3} \log (3 x+2)+\frac {14289}{125} \log (5 x+3) \]
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Rubi [A] time = 0.02, antiderivative size = 43, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {88} \[ \frac {4719}{125 (5 x+3)}-\frac {1331}{250 (5 x+3)^2}-\frac {343}{3} \log (3 x+2)+\frac {14289}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3}{(2+3 x) (3+5 x)^3} \, dx &=\int \left (-\frac {343}{2+3 x}+\frac {1331}{25 (3+5 x)^3}-\frac {4719}{25 (3+5 x)^2}+\frac {14289}{25 (3+5 x)}\right ) \, dx\\ &=-\frac {1331}{250 (3+5 x)^2}+\frac {4719}{125 (3+5 x)}-\frac {343}{3} \log (2+3 x)+\frac {14289}{125} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 44, normalized size = 1.02 \[ \frac {11 \left (4290 x+2598 (5 x+3)^2 \log (-3 (5 x+3))+2453\right )}{250 (5 x+3)^2}-\frac {343}{3} \log (3 x+2) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 55, normalized size = 1.28 \[ \frac {85734 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 85750 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (3 \, x + 2\right ) + 141570 \, x + 80949}{750 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.97, size = 33, normalized size = 0.77 \[ \frac {121 \, {\left (390 \, x + 223\right )}}{250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {14289}{125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {343}{3} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 36, normalized size = 0.84 \[ -\frac {343 \ln \left (3 x +2\right )}{3}+\frac {14289 \ln \left (5 x +3\right )}{125}-\frac {1331}{250 \left (5 x +3\right )^{2}}+\frac {4719}{125 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.45, size = 36, normalized size = 0.84 \[ \frac {121 \, {\left (390 \, x + 223\right )}}{250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {14289}{125} \, \log \left (5 \, x + 3\right ) - \frac {343}{3} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 29, normalized size = 0.67 \[ \frac {14289\,\ln \left (x+\frac {3}{5}\right )}{125}-\frac {343\,\ln \left (x+\frac {2}{3}\right )}{3}+\frac {\frac {4719\,x}{625}+\frac {26983}{6250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 36, normalized size = 0.84 \[ - \frac {- 47190 x - 26983}{6250 x^{2} + 7500 x + 2250} + \frac {14289 \log {\left (x + \frac {3}{5} \right )}}{125} - \frac {343 \log {\left (x + \frac {2}{3} \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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