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 = 0.0251528, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, 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*}
Mathematica [A] time = 0.0175599, 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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Maple [A] time = 0.008, size = 54, normalized size = 1. \begin{align*} -{\frac{7}{3\, \left ( 2+3\,x \right ) ^{3}}}-34\, \left ( 2+3\,x \right ) ^{-2}-505\, \left ( 2+3\,x \right ) ^{-1}-275\, \left ( 3+5\,x \right ) ^{-1}+3350\,\ln \left ( 2+3\,x \right ) -3350\,\ln \left ( 3+5\,x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09698, size = 76, normalized size = 1.38 \begin{align*} -\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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49365, size = 298, normalized size = 5.42 \begin{align*} -\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 )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.161504, size = 51, normalized size = 0.93 \begin{align*} - \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 )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.78946, size = 78, normalized size = 1.42 \begin{align*} -\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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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