Optimal. Leaf size=43 \[ \frac {343}{54 (2+3 x)^2}+\frac {1421}{27 (2+3 x)}-\frac {7189}{27} \log (2+3 x)+\frac {1331}{5} \log (3+5 x) \]
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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 {1421}{27 (3 x+2)}+\frac {343}{54 (3 x+2)^2}-\frac {7189}{27} \log (3 x+2)+\frac {1331}{5} \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 (3+5 x)} \, dx &=\int \left (-\frac {343}{9 (2+3 x)^3}-\frac {1421}{9 (2+3 x)^2}-\frac {7189}{9 (2+3 x)}+\frac {1331}{3+5 x}\right ) \, dx\\ &=\frac {343}{54 (2+3 x)^2}+\frac {1421}{27 (2+3 x)}-\frac {7189}{27} \log (2+3 x)+\frac {1331}{5} \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 39, normalized size = 0.91 \begin {gather*} \frac {49 (41+58 x)}{18 (2+3 x)^2}-\frac {7189}{27} \log (5 (2+3 x))+\frac {1331}{5} \log (3+5 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 36, normalized size = 0.84
method | result | size |
risch | \(\frac {\frac {1421 x}{9}+\frac {2009}{18}}{\left (2+3 x \right )^{2}}-\frac {7189 \ln \left (2+3 x \right )}{27}+\frac {1331 \ln \left (3+5 x \right )}{5}\) | \(32\) |
norman | \(\frac {-\frac {3185}{18} x -\frac {2009}{8} x^{2}}{\left (2+3 x \right )^{2}}-\frac {7189 \ln \left (2+3 x \right )}{27}+\frac {1331 \ln \left (3+5 x \right )}{5}\) | \(35\) |
default | \(\frac {343}{54 \left (2+3 x \right )^{2}}+\frac {1421}{27 \left (2+3 x \right )}-\frac {7189 \ln \left (2+3 x \right )}{27}+\frac {1331 \ln \left (3+5 x \right )}{5}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 36, normalized size = 0.84 \begin {gather*} \frac {49 \, {\left (58 \, x + 41\right )}}{18 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac {1331}{5} \, \log \left (5 \, x + 3\right ) - \frac {7189}{27} \, \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 = 0.40, size = 55, normalized size = 1.28 \begin {gather*} \frac {71874 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (5 \, x + 3\right ) - 71890 \, {\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 42630 \, x + 30135}{270 \, {\left (9 \, x^{2} + 12 \, x + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.15, size = 36, normalized size = 0.84 \begin {gather*} - \frac {- 2842 x - 2009}{162 x^{2} + 216 x + 72} + \frac {1331 \log {\left (x + \frac {3}{5} \right )}}{5} - \frac {7189 \log {\left (x + \frac {2}{3} \right )}}{27} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.70, size = 33, normalized size = 0.77 \begin {gather*} \frac {49 \, {\left (58 \, x + 41\right )}}{18 \, {\left (3 \, x + 2\right )}^{2}} + \frac {1331}{5} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {7189}{27} \, \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 {1331\,\ln \left (x+\frac {3}{5}\right )}{5}-\frac {7189\,\ln \left (x+\frac {2}{3}\right )}{27}+\frac {\frac {1421\,x}{81}+\frac {2009}{162}}{x^2+\frac {4\,x}{3}+\frac {4}{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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