Optimal. Leaf size=50 \[ -\frac {3136}{9 (3 x+2)}-\frac {1331}{5 (5 x+3)}-\frac {343}{18 (3 x+2)^2}+2541 \log (3 x+2)-2541 \log (5 x+3) \]
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Rubi [A] time = 0.03, antiderivative size = 50, 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} \[ -\frac {3136}{9 (3 x+2)}-\frac {1331}{5 (5 x+3)}-\frac {343}{18 (3 x+2)^2}+2541 \log (3 x+2)-2541 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3}{(2+3 x)^3 (3+5 x)^2} \, dx &=\int \left (\frac {343}{3 (2+3 x)^3}+\frac {3136}{3 (2+3 x)^2}+\frac {7623}{2+3 x}+\frac {1331}{(3+5 x)^2}-\frac {12705}{3+5 x}\right ) \, dx\\ &=-\frac {343}{18 (2+3 x)^2}-\frac {3136}{9 (2+3 x)}-\frac {1331}{5 (3+5 x)}+2541 \log (2+3 x)-2541 \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.04, size = 47, normalized size = 0.94 \[ -\frac {686022 x^2+891911 x+289137}{90 (3 x+2)^2 (5 x+3)}+2541 \log (5 (3 x+2))-2541 \log (5 x+3) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 75, normalized size = 1.50 \[ -\frac {686022 \, x^{2} + 228690 \, {\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (5 \, x + 3\right ) - 228690 \, {\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (3 \, x + 2\right ) + 891911 \, x + 289137}{90 \, {\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 49, normalized size = 0.98 \[ -\frac {1331}{5 \, {\left (5 \, x + 3\right )}} + \frac {245 \, {\left (\frac {66}{5 \, x + 3} + 163\right )}}{2 \, {\left (\frac {1}{5 \, x + 3} + 3\right )}^{2}} + 2541 \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 45, normalized size = 0.90 \[ 2541 \ln \left (3 x +2\right )-2541 \ln \left (5 x +3\right )-\frac {343}{18 \left (3 x +2\right )^{2}}-\frac {3136}{9 \left (3 x +2\right )}-\frac {1331}{5 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 46, normalized size = 0.92 \[ -\frac {686022 \, x^{2} + 891911 \, x + 289137}{90 \, {\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )}} - 2541 \, \log \left (5 \, x + 3\right ) + 2541 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 36, normalized size = 0.72 \[ 5082\,\mathrm {atanh}\left (30\,x+19\right )-\frac {\frac {114337\,x^2}{675}+\frac {891911\,x}{4050}+\frac {96379}{1350}}{x^3+\frac {29\,x^2}{15}+\frac {56\,x}{45}+\frac {4}{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 41, normalized size = 0.82 \[ - \frac {686022 x^{2} + 891911 x + 289137}{4050 x^{3} + 7830 x^{2} + 5040 x + 1080} - 2541 \log {\left (x + \frac {3}{5} \right )} + 2541 \log {\left (x + \frac {2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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