Optimal. Leaf size=88 \[ \frac{424975}{3 x+2}+\frac{277750}{5 x+3}+\frac{28555}{(3 x+2)^2}-\frac{15125}{2 (5 x+3)^2}+\frac{6934}{3 (3 x+2)^3}+\frac{707}{4 (3 x+2)^4}+\frac{49}{5 (3 x+2)^5}-2958125 \log (3 x+2)+2958125 \log (5 x+3) \]
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Rubi [A] time = 0.0459891, antiderivative size = 88, normalized size of antiderivative = 1., 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} \[ \frac{424975}{3 x+2}+\frac{277750}{5 x+3}+\frac{28555}{(3 x+2)^2}-\frac{15125}{2 (5 x+3)^2}+\frac{6934}{3 (3 x+2)^3}+\frac{707}{4 (3 x+2)^4}+\frac{49}{5 (3 x+2)^5}-2958125 \log (3 x+2)+2958125 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2}{(2+3 x)^6 (3+5 x)^3} \, dx &=\int \left (-\frac{147}{(2+3 x)^6}-\frac{2121}{(2+3 x)^5}-\frac{20802}{(2+3 x)^4}-\frac{171330}{(2+3 x)^3}-\frac{1274925}{(2+3 x)^2}-\frac{8874375}{2+3 x}+\frac{75625}{(3+5 x)^3}-\frac{1388750}{(3+5 x)^2}+\frac{14790625}{3+5 x}\right ) \, dx\\ &=\frac{49}{5 (2+3 x)^5}+\frac{707}{4 (2+3 x)^4}+\frac{6934}{3 (2+3 x)^3}+\frac{28555}{(2+3 x)^2}+\frac{424975}{2+3 x}-\frac{15125}{2 (3+5 x)^2}+\frac{277750}{3+5 x}-2958125 \log (2+3 x)+2958125 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.063002, size = 90, normalized size = 1.02 \[ \frac{424975}{3 x+2}+\frac{277750}{5 x+3}+\frac{28555}{(3 x+2)^2}-\frac{15125}{2 (5 x+3)^2}+\frac{6934}{3 (3 x+2)^3}+\frac{707}{4 (3 x+2)^4}+\frac{49}{5 (3 x+2)^5}-2958125 \log (5 (3 x+2))+2958125 \log (5 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 81, normalized size = 0.9 \begin{align*}{\frac{49}{5\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{707}{4\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{6934}{3\, \left ( 2+3\,x \right ) ^{3}}}+28555\, \left ( 2+3\,x \right ) ^{-2}+424975\, \left ( 2+3\,x \right ) ^{-1}-{\frac{15125}{2\, \left ( 3+5\,x \right ) ^{2}}}+277750\, \left ( 3+5\,x \right ) ^{-1}-2958125\,\ln \left ( 2+3\,x \right ) +2958125\,\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 = 1.03018, size = 116, normalized size = 1.32 \begin{align*} \frac{71882437500 \, x^{6} + 280341506250 \, x^{5} + 455361930000 \, x^{4} + 394308004875 \, x^{3} + 191974077080 \, x^{2} + 49825144515 \, x + 5385650262}{60 \,{\left (6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right )}} + 2958125 \, \log \left (5 \, x + 3\right ) - 2958125 \, \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 = 1.31756, size = 590, normalized size = 6.7 \begin{align*} \frac{71882437500 \, x^{6} + 280341506250 \, x^{5} + 455361930000 \, x^{4} + 394308004875 \, x^{3} + 191974077080 \, x^{2} + 177487500 \,{\left (6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right )} \log \left (5 \, x + 3\right ) - 177487500 \,{\left (6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right )} \log \left (3 \, x + 2\right ) + 49825144515 \, x + 5385650262}{60 \,{\left (6075 \, x^{7} + 27540 \, x^{6} + 53487 \, x^{5} + 57690 \, x^{4} + 37320 \, x^{3} + 14480 \, x^{2} + 3120 \, x + 288\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.212291, size = 82, normalized size = 0.93 \begin{align*} \frac{71882437500 x^{6} + 280341506250 x^{5} + 455361930000 x^{4} + 394308004875 x^{3} + 191974077080 x^{2} + 49825144515 x + 5385650262}{364500 x^{7} + 1652400 x^{6} + 3209220 x^{5} + 3461400 x^{4} + 2239200 x^{3} + 868800 x^{2} + 187200 x + 17280} + 2958125 \log{\left (x + \frac{3}{5} \right )} - 2958125 \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 = 2.42009, size = 88, normalized size = 1. \begin{align*} \frac{71882437500 \, x^{6} + 280341506250 \, x^{5} + 455361930000 \, x^{4} + 394308004875 \, x^{3} + 191974077080 \, x^{2} + 49825144515 \, x + 5385650262}{60 \,{\left (5 \, x + 3\right )}^{2}{\left (3 \, x + 2\right )}^{5}} + 2958125 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 2958125 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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