Optimal. Leaf size=57 \[ \frac{707}{3 x+2}+\frac{1133}{5 x+3}+\frac{49}{2 (3 x+2)^2}-\frac{121}{2 (5 x+3)^2}-6934 \log (3 x+2)+6934 \log (5 x+3) \]
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Rubi [A] time = 0.0288247, antiderivative size = 57, 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} \[ \frac{707}{3 x+2}+\frac{1133}{5 x+3}+\frac{49}{2 (3 x+2)^2}-\frac{121}{2 (5 x+3)^2}-6934 \log (3 x+2)+6934 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2}{(2+3 x)^3 (3+5 x)^3} \, dx &=\int \left (-\frac{147}{(2+3 x)^3}-\frac{2121}{(2+3 x)^2}-\frac{20802}{2+3 x}+\frac{605}{(3+5 x)^3}-\frac{5665}{(3+5 x)^2}+\frac{34670}{3+5 x}\right ) \, dx\\ &=\frac{49}{2 (2+3 x)^2}+\frac{707}{2+3 x}-\frac{121}{2 (3+5 x)^2}+\frac{1133}{3+5 x}-6934 \log (2+3 x)+6934 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.026, size = 59, normalized size = 1.04 \[ \frac{707}{3 x+2}+\frac{1133}{5 x+3}+\frac{49}{2 (3 x+2)^2}-\frac{121}{2 (5 x+3)^2}-6934 \log (5 (3 x+2))+6934 \log (5 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 54, normalized size = 1. \begin{align*}{\frac{49}{2\, \left ( 2+3\,x \right ) ^{2}}}+707\, \left ( 2+3\,x \right ) ^{-1}-{\frac{121}{2\, \left ( 3+5\,x \right ) ^{2}}}+1133\, \left ( 3+5\,x \right ) ^{-1}-6934\,\ln \left ( 2+3\,x \right ) +6934\,\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 = 3.10172, size = 76, normalized size = 1.33 \begin{align*} \frac{208020 \, x^{3} + 395238 \, x^{2} + 249932 \, x + 52601}{2 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} + 6934 \, \log \left (5 \, x + 3\right ) - 6934 \, \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 = 1.25557, size = 298, normalized size = 5.23 \begin{align*} \frac{208020 \, x^{3} + 395238 \, x^{2} + 13868 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (5 \, x + 3\right ) - 13868 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (3 \, x + 2\right ) + 249932 \, x + 52601}{2 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.163014, size = 51, normalized size = 0.89 \begin{align*} \frac{208020 x^{3} + 395238 x^{2} + 249932 x + 52601}{450 x^{4} + 1140 x^{3} + 1082 x^{2} + 456 x + 72} + 6934 \log{\left (x + \frac{3}{5} \right )} - 6934 \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 = 1.67244, size = 65, normalized size = 1.14 \begin{align*} \frac{208020 \, x^{3} + 395238 \, x^{2} + 249932 \, x + 52601}{2 \,{\left (15 \, x^{2} + 19 \, x + 6\right )}^{2}} + 6934 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 6934 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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