Optimal. Leaf size=46 \[ -\frac {68}{3 x+2}-\frac {55}{5 x+3}-\frac {7}{2 (3 x+2)^2}+505 \log (3 x+2)-505 \log (5 x+3) \]
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Rubi [A] time = 0.02, antiderivative size = 46, 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} \begin {gather*} -\frac {68}{3 x+2}-\frac {55}{5 x+3}-\frac {7}{2 (3 x+2)^2}+505 \log (3 x+2)-505 \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {1-2 x}{(2+3 x)^3 (3+5 x)^2} \, dx &=\int \left (\frac {21}{(2+3 x)^3}+\frac {204}{(2+3 x)^2}+\frac {1515}{2+3 x}+\frac {275}{(3+5 x)^2}-\frac {2525}{3+5 x}\right ) \, dx\\ &=-\frac {7}{2 (2+3 x)^2}-\frac {68}{2+3 x}-\frac {55}{3+5 x}+505 \log (2+3 x)-505 \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 48, normalized size = 1.04 \begin {gather*} -\frac {68}{3 x+2}-\frac {55}{5 x+3}-\frac {7}{2 (3 x+2)^2}+505 \log (3 x+2)-505 \log (-3 (5 x+3)) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1-2 x}{(2+3 x)^3 (3+5 x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.33, size = 75, normalized size = 1.63 \begin {gather*} -\frac {3030 \, x^{2} + 1010 \, {\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (5 \, x + 3\right ) - 1010 \, {\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (3 \, x + 2\right ) + 3939 \, x + 1277}{2 \, {\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.31, size = 49, normalized size = 1.07 \begin {gather*} -\frac {55}{5 \, x + 3} + \frac {15 \, {\left (\frac {206}{5 \, x + 3} + 513\right )}}{2 \, {\left (\frac {1}{5 \, x + 3} + 3\right )}^{2}} + 505 \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 45, normalized size = 0.98 \begin {gather*} 505 \ln \left (3 x +2\right )-505 \ln \left (5 x +3\right )-\frac {7}{2 \left (3 x +2\right )^{2}}-\frac {68}{3 x +2}-\frac {55}{5 x +3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 46, normalized size = 1.00 \begin {gather*} -\frac {3030 \, x^{2} + 3939 \, x + 1277}{2 \, {\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )}} - 505 \, \log \left (5 \, x + 3\right ) + 505 \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 36, normalized size = 0.78 \begin {gather*} 1010\,\mathrm {atanh}\left (30\,x+19\right )-\frac {\frac {101\,x^2}{3}+\frac {1313\,x}{30}+\frac {1277}{90}}{x^3+\frac {29\,x^2}{15}+\frac {56\,x}{45}+\frac {4}{15}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 41, normalized size = 0.89 \begin {gather*} - \frac {3030 x^{2} + 3939 x + 1277}{90 x^{3} + 174 x^{2} + 112 x + 24} - 505 \log {\left (x + \frac {3}{5} \right )} + 505 \log {\left (x + \frac {2}{3} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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