Optimal. Leaf size=39 \[ -\frac {49}{3 (3 x+2)}-\frac {121}{5 (5 x+3)}+154 \log (3 x+2)-154 \log (5 x+3) \]
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Rubi [A] time = 0.02, antiderivative size = 39, 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} \[ -\frac {49}{3 (3 x+2)}-\frac {121}{5 (5 x+3)}+154 \log (3 x+2)-154 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2}{(2+3 x)^2 (3+5 x)^2} \, dx &=\int \left (\frac {49}{(2+3 x)^2}+\frac {462}{2+3 x}+\frac {121}{(3+5 x)^2}-\frac {770}{3+5 x}\right ) \, dx\\ &=-\frac {49}{3 (2+3 x)}-\frac {121}{5 (3+5 x)}+154 \log (2+3 x)-154 \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.05, size = 61, normalized size = 1.56 \[ -\frac {-2310 \left (15 x^2+19 x+6\right ) \log (5 (3 x+2))+2310 \left (15 x^2+19 x+6\right ) \log (5 x+3)+2314 x+1461}{15 (3 x+2) (5 x+3)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 55, normalized size = 1.41 \[ -\frac {2310 \, {\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (5 \, x + 3\right ) - 2310 \, {\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (3 \, x + 2\right ) + 2314 \, x + 1461}{15 \, {\left (15 \, x^{2} + 19 \, x + 6\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.86, size = 38, normalized size = 0.97 \[ -\frac {121}{5 \, {\left (5 \, x + 3\right )}} + \frac {245}{\frac {1}{5 \, x + 3} + 3} + 154 \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 36, normalized size = 0.92 \[ 154 \ln \left (3 x +2\right )-154 \ln \left (5 x +3\right )-\frac {49}{3 \left (3 x +2\right )}-\frac {121}{5 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 36, normalized size = 0.92 \[ -\frac {2314 \, x + 1461}{15 \, {\left (15 \, x^{2} + 19 \, x + 6\right )}} - 154 \, \log \left (5 \, x + 3\right ) + 154 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 26, normalized size = 0.67 \[ 308\,\mathrm {atanh}\left (30\,x+19\right )-\frac {\frac {2314\,x}{225}+\frac {487}{75}}{x^2+\frac {19\,x}{15}+\frac {2}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 32, normalized size = 0.82 \[ \frac {- 2314 x - 1461}{225 x^{2} + 285 x + 90} - 154 \log {\left (x + \frac {3}{5} \right )} + 154 \log {\left (x + \frac {2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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