Optimal. Leaf size=43 \[ -\frac {1331}{250 (3+5 x)^2}+\frac {4719}{125 (3+5 x)}-\frac {343}{3} \log (2+3 x)+\frac {14289}{125} \log (3+5 x) \]
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Rubi [A]
time = 0.01, 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 = {90}
\begin {gather*} \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) \end {gather*}
Antiderivative was successfully verified.
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Rule 90
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 = 0.02, size = 44, normalized size = 1.02 \begin {gather*} -\frac {343}{3} \log (2+3 x)+\frac {11 \left (2453+4290 x+2598 (3+5 x)^2 \log (-3 (3+5 x))\right )}{250 (3+5 x)^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 36, normalized size = 0.84
method | result | size |
risch | \(\frac {\frac {4719 x}{25}+\frac {26983}{250}}{\left (3+5 x \right )^{2}}-\frac {343 \ln \left (2+3 x \right )}{3}+\frac {14289 \ln \left (3+5 x \right )}{125}\) | \(32\) |
norman | \(\frac {-\frac {12826}{75} x -\frac {26983}{90} x^{2}}{\left (3+5 x \right )^{2}}-\frac {343 \ln \left (2+3 x \right )}{3}+\frac {14289 \ln \left (3+5 x \right )}{125}\) | \(35\) |
default | \(-\frac {1331}{250 \left (3+5 x \right )^{2}}+\frac {4719}{125 \left (3+5 x \right )}-\frac {343 \ln \left (2+3 x \right )}{3}+\frac {14289 \ln \left (3+5 x \right )}{125}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 36, normalized size = 0.84 \begin {gather*} \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 ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.44, size = 55, normalized size = 1.28 \begin {gather*} \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 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 36, normalized size = 0.84 \begin {gather*} - \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.56, size = 33, normalized size = 0.77 \begin {gather*} \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 ) \end {gather*}
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 \begin {gather*} \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}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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