Optimal. Leaf size=90 \[ -\frac{277750}{3 x+2}-\frac{75625}{5 x+3}-\frac{46475}{2 (3 x+2)^2}-\frac{7480}{3 (3 x+2)^3}-\frac{1133}{4 (3 x+2)^4}-\frac{154}{5 (3 x+2)^5}-\frac{49}{18 (3 x+2)^6}+1615625 \log (3 x+2)-1615625 \log (5 x+3) \]
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Rubi [A] time = 0.0423518, antiderivative size = 90, 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} \[ -\frac{277750}{3 x+2}-\frac{75625}{5 x+3}-\frac{46475}{2 (3 x+2)^2}-\frac{7480}{3 (3 x+2)^3}-\frac{1133}{4 (3 x+2)^4}-\frac{154}{5 (3 x+2)^5}-\frac{49}{18 (3 x+2)^6}+1615625 \log (3 x+2)-1615625 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2}{(2+3 x)^7 (3+5 x)^2} \, dx &=\int \left (\frac{49}{(2+3 x)^7}+\frac{462}{(2+3 x)^6}+\frac{3399}{(2+3 x)^5}+\frac{22440}{(2+3 x)^4}+\frac{139425}{(2+3 x)^3}+\frac{833250}{(2+3 x)^2}+\frac{4846875}{2+3 x}+\frac{378125}{(3+5 x)^2}-\frac{8078125}{3+5 x}\right ) \, dx\\ &=-\frac{49}{18 (2+3 x)^6}-\frac{154}{5 (2+3 x)^5}-\frac{1133}{4 (2+3 x)^4}-\frac{7480}{3 (2+3 x)^3}-\frac{46475}{2 (2+3 x)^2}-\frac{277750}{2+3 x}-\frac{75625}{3+5 x}+1615625 \log (2+3 x)-1615625 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0881267, size = 92, normalized size = 1.02 \[ -\frac{277750}{3 x+2}-\frac{75625}{5 x+3}-\frac{46475}{2 (3 x+2)^2}-\frac{7480}{3 (3 x+2)^3}-\frac{1133}{4 (3 x+2)^4}-\frac{154}{5 (3 x+2)^5}-\frac{49}{18 (3 x+2)^6}+1615625 \log (5 (3 x+2))-1615625 \log (5 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 81, normalized size = 0.9 \begin{align*} -{\frac{49}{18\, \left ( 2+3\,x \right ) ^{6}}}-{\frac{154}{5\, \left ( 2+3\,x \right ) ^{5}}}-{\frac{1133}{4\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{7480}{3\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{46475}{2\, \left ( 2+3\,x \right ) ^{2}}}-277750\, \left ( 2+3\,x \right ) ^{-1}-75625\, \left ( 3+5\,x \right ) ^{-1}+1615625\,\ln \left ( 2+3\,x \right ) -1615625\,\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 = 1.13944, size = 116, normalized size = 1.29 \begin{align*} -\frac{70667437500 \, x^{6} + 280314168750 \, x^{5} + 463211966250 \, x^{4} + 408159415125 \, x^{3} + 202262350455 \, x^{2} + 53445037346 \, x + 5882909754}{180 \,{\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )}} - 1615625 \, \log \left (5 \, x + 3\right ) + 1615625 \, \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 = 1.28323, size = 589, normalized size = 6.54 \begin{align*} -\frac{70667437500 \, x^{6} + 280314168750 \, x^{5} + 463211966250 \, x^{4} + 408159415125 \, x^{3} + 202262350455 \, x^{2} + 290812500 \,{\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )} \log \left (5 \, x + 3\right ) - 290812500 \,{\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )} \log \left (3 \, x + 2\right ) + 53445037346 \, x + 5882909754}{180 \,{\left (3645 \, x^{7} + 16767 \, x^{6} + 33048 \, x^{5} + 36180 \, x^{4} + 23760 \, x^{3} + 9360 \, x^{2} + 2048 \, x + 192\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.211946, size = 82, normalized size = 0.91 \begin{align*} - \frac{70667437500 x^{6} + 280314168750 x^{5} + 463211966250 x^{4} + 408159415125 x^{3} + 202262350455 x^{2} + 53445037346 x + 5882909754}{656100 x^{7} + 3018060 x^{6} + 5948640 x^{5} + 6512400 x^{4} + 4276800 x^{3} + 1684800 x^{2} + 368640 x + 34560} - 1615625 \log{\left (x + \frac{3}{5} \right )} + 1615625 \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 = 2.87296, size = 115, normalized size = 1.28 \begin{align*} -\frac{75625}{5 \, x + 3} + \frac{625 \,{\left (\frac{22074930}{5 \, x + 3} + \frac{16294797}{{\left (5 \, x + 3\right )}^{2}} + \frac{6120660}{{\left (5 \, x + 3\right )}^{3}} + \frac{1179210}{{\left (5 \, x + 3\right )}^{4}} + \frac{94660}{{\left (5 \, x + 3\right )}^{5}} + 12117357\right )}}{4 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}^{6}} + 1615625 \, \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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