Optimal. Leaf size=57 \[ -\frac {2541}{3 x+2}-\frac {1331}{5 x+3}-\frac {1568}{9 (3 x+2)^2}-\frac {343}{27 (3 x+2)^3}+16698 \log (3 x+2)-16698 \log (5 x+3) \]
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Rubi [A] time = 0.03, antiderivative size = 57, 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} \[ -\frac {2541}{3 x+2}-\frac {1331}{5 x+3}-\frac {1568}{9 (3 x+2)^2}-\frac {343}{27 (3 x+2)^3}+16698 \log (3 x+2)-16698 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3}{(2+3 x)^4 (3+5 x)^2} \, dx &=\int \left (\frac {343}{3 (2+3 x)^4}+\frac {3136}{3 (2+3 x)^3}+\frac {7623}{(2+3 x)^2}+\frac {50094}{2+3 x}+\frac {6655}{(3+5 x)^2}-\frac {83490}{3+5 x}\right ) \, dx\\ &=-\frac {343}{27 (2+3 x)^3}-\frac {1568}{9 (2+3 x)^2}-\frac {2541}{2+3 x}-\frac {1331}{3+5 x}+16698 \log (2+3 x)-16698 \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.04, size = 59, normalized size = 1.04 \[ -\frac {2541}{3 x+2}-\frac {1331}{5 x+3}-\frac {1568}{9 (3 x+2)^2}-\frac {343}{27 (3 x+2)^3}+16698 \log (5 (3 x+2))-16698 \log (5 x+3) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 95, normalized size = 1.67 \[ -\frac {4057614 \, x^{3} + 7979967 \, x^{2} + 450846 \, {\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (5 \, x + 3\right ) - 450846 \, {\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (3 \, x + 2\right ) + 5226815 \, x + 1140033}{27 \, {\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.88, size = 58, normalized size = 1.02 \[ -\frac {1331}{5 \, x + 3} + \frac {35 \, {\left (\frac {11119}{5 \, x + 3} + \frac {2244}{{\left (5 \, x + 3\right )}^{2}} + 14386\right )}}{{\left (\frac {1}{5 \, x + 3} + 3\right )}^{3}} + 16698 \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 54, normalized size = 0.95 \[ 16698 \ln \left (3 x +2\right )-16698 \ln \left (5 x +3\right )-\frac {343}{27 \left (3 x +2\right )^{3}}-\frac {1568}{9 \left (3 x +2\right )^{2}}-\frac {2541}{3 x +2}-\frac {1331}{5 x +3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 56, normalized size = 0.98 \[ -\frac {4057614 \, x^{3} + 7979967 \, x^{2} + 5226815 \, x + 1140033}{27 \, {\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} - 16698 \, \log \left (5 \, x + 3\right ) + 16698 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.79, size = 46, normalized size = 0.81 \[ 33396\,\mathrm {atanh}\left (30\,x+19\right )-\frac {\frac {5566\,x^3}{5}+\frac {886663\,x^2}{405}+\frac {1045363\,x}{729}+\frac {380011}{1215}}{x^4+\frac {13\,x^3}{5}+\frac {38\,x^2}{15}+\frac {148\,x}{135}+\frac {8}{45}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 51, normalized size = 0.89 \[ - \frac {4057614 x^{3} + 7979967 x^{2} + 5226815 x + 1140033}{3645 x^{4} + 9477 x^{3} + 9234 x^{2} + 3996 x + 648} - 16698 \log {\left (x + \frac {3}{5} \right )} + 16698 \log {\left (x + \frac {2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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