Optimal. Leaf size=32 \[ -\frac {121}{25 (5 x+3)}+\frac {49}{3} \log (3 x+2)-\frac {407}{25} \log (5 x+3) \]
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Rubi [A] time = 0.01, antiderivative size = 32, normalized size of antiderivative = 1.00, 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} \[ -\frac {121}{25 (5 x+3)}+\frac {49}{3} \log (3 x+2)-\frac {407}{25} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2}{(2+3 x) (3+5 x)^2} \, dx &=\int \left (\frac {49}{2+3 x}+\frac {121}{5 (3+5 x)^2}-\frac {407}{5 (3+5 x)}\right ) \, dx\\ &=-\frac {121}{25 (3+5 x)}+\frac {49}{3} \log (2+3 x)-\frac {407}{25} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 32, normalized size = 1.00 \[ -\frac {121}{125 x+75}+\frac {49}{3} \log (3 x+2)-\frac {407}{25} \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 37, normalized size = 1.16 \[ -\frac {1221 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 1225 \, {\left (5 \, x + 3\right )} \log \left (3 \, x + 2\right ) + 363}{75 \, {\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.06, size = 43, normalized size = 1.34 \[ -\frac {121}{25 \, {\left (5 \, x + 3\right )}} - \frac {4}{75} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) + \frac {49}{3} \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 27, normalized size = 0.84 \[ \frac {49 \ln \left (3 x +2\right )}{3}-\frac {407 \ln \left (5 x +3\right )}{25}-\frac {121}{25 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 26, normalized size = 0.81 \[ -\frac {121}{25 \, {\left (5 \, x + 3\right )}} - \frac {407}{25} \, \log \left (5 \, x + 3\right ) + \frac {49}{3} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.10, size = 22, normalized size = 0.69 \[ \frac {49\,\ln \left (x+\frac {2}{3}\right )}{3}-\frac {407\,\ln \left (x+\frac {3}{5}\right )}{25}-\frac {121}{125\,\left (x+\frac {3}{5}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 26, normalized size = 0.81 \[ - \frac {407 \log {\left (x + \frac {3}{5} \right )}}{25} + \frac {49 \log {\left (x + \frac {2}{3} \right )}}{3} - \frac {121}{125 x + 75} \]
Verification of antiderivative is not currently implemented for this CAS.
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