Optimal. Leaf size=55 \[ -\frac {505}{3 x+2}-\frac {275}{5 x+3}-\frac {34}{(3 x+2)^2}-\frac {7}{3 (3 x+2)^3}+3350 \log (3 x+2)-3350 \log (5 x+3) \]
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Rubi [A] time = 0.03, antiderivative size = 55, 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} \[ -\frac {505}{3 x+2}-\frac {275}{5 x+3}-\frac {34}{(3 x+2)^2}-\frac {7}{3 (3 x+2)^3}+3350 \log (3 x+2)-3350 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {1-2 x}{(2+3 x)^4 (3+5 x)^2} \, dx &=\int \left (\frac {21}{(2+3 x)^4}+\frac {204}{(2+3 x)^3}+\frac {1515}{(2+3 x)^2}+\frac {10050}{2+3 x}+\frac {1375}{(3+5 x)^2}-\frac {16750}{3+5 x}\right ) \, dx\\ &=-\frac {7}{3 (2+3 x)^3}-\frac {34}{(2+3 x)^2}-\frac {505}{2+3 x}-\frac {275}{3+5 x}+3350 \log (2+3 x)-3350 \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.04, size = 57, normalized size = 1.04 \[ -\frac {505}{3 x+2}-\frac {275}{5 x+3}-\frac {34}{(3 x+2)^2}-\frac {7}{3 (3 x+2)^3}+3350 \log (3 x+2)-3350 \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 95, normalized size = 1.73 \[ -\frac {90450 \, x^{3} + 177885 \, x^{2} + 10050 \, {\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (5 \, x + 3\right ) - 10050 \, {\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (3 \, x + 2\right ) + 116513 \, x + 25413}{3 \, {\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.20, size = 58, normalized size = 1.05 \[ -\frac {275}{5 \, x + 3} + \frac {225 \, {\left (\frac {339}{5 \, x + 3} + \frac {68}{{\left (5 \, x + 3\right )}^{2}} + 440\right )}}{{\left (\frac {1}{5 \, x + 3} + 3\right )}^{3}} + 3350 \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 54, normalized size = 0.98 \[ 3350 \ln \left (3 x +2\right )-3350 \ln \left (5 x +3\right )-\frac {7}{3 \left (3 x +2\right )^{3}}-\frac {34}{\left (3 x +2\right )^{2}}-\frac {505}{3 x +2}-\frac {275}{5 x +3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 56, normalized size = 1.02 \[ -\frac {90450 \, x^{3} + 177885 \, x^{2} + 116513 \, x + 25413}{3 \, {\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} - 3350 \, \log \left (5 \, x + 3\right ) + 3350 \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.11, size = 46, normalized size = 0.84 \[ 6700\,\mathrm {atanh}\left (30\,x+19\right )-\frac {\frac {670\,x^3}{3}+\frac {3953\,x^2}{9}+\frac {116513\,x}{405}+\frac {8471}{135}}{x^4+\frac {13\,x^3}{5}+\frac {38\,x^2}{15}+\frac {148\,x}{135}+\frac {8}{45}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 51, normalized size = 0.93 \[ - \frac {90450 x^{3} + 177885 x^{2} + 116513 x + 25413}{405 x^{4} + 1053 x^{3} + 1026 x^{2} + 444 x + 72} - 3350 \log {\left (x + \frac {3}{5} \right )} + 3350 \log {\left (x + \frac {2}{3} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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