Optimal. Leaf size=35 \[ -\frac {7}{3 x+2}-\frac {11}{5 x+3}+68 \log (3 x+2)-68 \log (5 x+3) \]
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Rubi [A] time = 0.02, antiderivative size = 35, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ -\frac {7}{3 x+2}-\frac {11}{5 x+3}+68 \log (3 x+2)-68 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {1-2 x}{(2+3 x)^2 (3+5 x)^2} \, dx &=\int \left (\frac {21}{(2+3 x)^2}+\frac {204}{2+3 x}+\frac {55}{(3+5 x)^2}-\frac {340}{3+5 x}\right ) \, dx\\ &=-\frac {7}{2+3 x}-\frac {11}{3+5 x}+68 \log (2+3 x)-68 \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 37, normalized size = 1.06 \[ -\frac {7}{3 x+2}-\frac {11}{5 x+3}+68 \log (3 x+2)-68 \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 55, normalized size = 1.57 \[ -\frac {68 \, {\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (5 \, x + 3\right ) - 68 \, {\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (3 \, x + 2\right ) + 68 \, x + 43}{15 \, x^{2} + 19 \, x + 6} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.26, size = 38, normalized size = 1.09 \[ -\frac {11}{5 \, x + 3} + \frac {105}{\frac {1}{5 \, x + 3} + 3} + 68 \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 36, normalized size = 1.03 \[ 68 \ln \left (3 x +2\right )-68 \ln \left (5 x +3\right )-\frac {7}{3 x +2}-\frac {11}{5 x +3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.70, size = 36, normalized size = 1.03 \[ -\frac {68 \, x + 43}{15 \, x^{2} + 19 \, x + 6} - 68 \, \log \left (5 \, x + 3\right ) + 68 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.11, size = 26, normalized size = 0.74 \[ 136\,\mathrm {atanh}\left (30\,x+19\right )-\frac {\frac {68\,x}{15}+\frac {43}{15}}{x^2+\frac {19\,x}{15}+\frac {2}{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 31, normalized size = 0.89 \[ - \frac {68 x + 43}{15 x^{2} + 19 x + 6} - 68 \log {\left (x + \frac {3}{5} \right )} + 68 \log {\left (x + \frac {2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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