Optimal. Leaf size=48 \[ \frac {81 x}{100}+\frac {2401}{968 (1-2 x)}-\frac {1}{15125 (5 x+3)}+\frac {10633 \log (1-2 x)}{5324}+\frac {136 \log (5 x+3)}{166375} \]
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Rubi [A] time = 0.02, antiderivative size = 48, 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} \[ \frac {81 x}{100}+\frac {2401}{968 (1-2 x)}-\frac {1}{15125 (5 x+3)}+\frac {10633 \log (1-2 x)}{5324}+\frac {136 \log (5 x+3)}{166375} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^4}{(1-2 x)^2 (3+5 x)^2} \, dx &=\int \left (\frac {81}{100}+\frac {2401}{484 (-1+2 x)^2}+\frac {10633}{2662 (-1+2 x)}+\frac {1}{3025 (3+5 x)^2}+\frac {136}{33275 (3+5 x)}\right ) \, dx\\ &=\frac {2401}{968 (1-2 x)}+\frac {81 x}{100}-\frac {1}{15125 (3+5 x)}+\frac {10633 \log (1-2 x)}{5324}+\frac {136 \log (3+5 x)}{166375}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 47, normalized size = 0.98 \[ \frac {-\frac {11 (1500641 x+900367)}{10 x^2+x-3}+359370 (3 x+2)+2658250 \log (3-6 x)+1088 \log (-3 (5 x+3))}{1331000} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 59, normalized size = 1.23 \[ \frac {10781100 \, x^{3} + 1078110 \, x^{2} + 1088 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) + 2658250 \, {\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 19741381 \, x - 9904037}{1331000 \, {\left (10 \, x^{2} + x - 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.20, size = 74, normalized size = 1.54 \[ \frac {{\left (5 \, x + 3\right )} {\left (\frac {1343273}{5 \, x + 3} - 107811\right )}}{332750 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}} - \frac {1}{15125 \, {\left (5 \, x + 3\right )}} - \frac {999}{500} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) + \frac {10633}{5324} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 39, normalized size = 0.81 \[ \frac {81 x}{100}+\frac {10633 \ln \left (2 x -1\right )}{5324}+\frac {136 \ln \left (5 x +3\right )}{166375}-\frac {1}{15125 \left (5 x +3\right )}-\frac {2401}{968 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 37, normalized size = 0.77 \[ \frac {81}{100} \, x - \frac {1500641 \, x + 900367}{121000 \, {\left (10 \, x^{2} + x - 3\right )}} + \frac {136}{166375} \, \log \left (5 \, x + 3\right ) + \frac {10633}{5324} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.07, size = 33, normalized size = 0.69 \[ \frac {81\,x}{100}+\frac {10633\,\ln \left (x-\frac {1}{2}\right )}{5324}+\frac {136\,\ln \left (x+\frac {3}{5}\right )}{166375}-\frac {\frac {1500641\,x}{1210000}+\frac {900367}{1210000}}{x^2+\frac {x}{10}-\frac {3}{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 41, normalized size = 0.85 \[ \frac {81 x}{100} + \frac {- 1500641 x - 900367}{1210000 x^{2} + 121000 x - 363000} + \frac {10633 \log {\left (x - \frac {1}{2} \right )}}{5324} + \frac {136 \log {\left (x + \frac {3}{5} \right )}}{166375} \]
Verification of antiderivative is not currently implemented for this CAS.
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