Optimal. Leaf size=48 \[ -\frac{81 x}{250}-\frac{134}{75625 (5 x+3)}-\frac{1}{13750 (5 x+3)^2}-\frac{2401 \log (1-2 x)}{5324}+\frac{6802 \log (5 x+3)}{831875} \]
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Rubi [A] time = 0.0211931, antiderivative size = 48, 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} \[ -\frac{81 x}{250}-\frac{134}{75625 (5 x+3)}-\frac{1}{13750 (5 x+3)^2}-\frac{2401 \log (1-2 x)}{5324}+\frac{6802 \log (5 x+3)}{831875} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^4}{(1-2 x) (3+5 x)^3} \, dx &=\int \left (-\frac{81}{250}-\frac{2401}{2662 (-1+2 x)}+\frac{1}{1375 (3+5 x)^3}+\frac{134}{15125 (3+5 x)^2}+\frac{6802}{166375 (3+5 x)}\right ) \, dx\\ &=-\frac{81 x}{250}-\frac{1}{13750 (3+5 x)^2}-\frac{134}{75625 (3+5 x)}-\frac{2401 \log (1-2 x)}{5324}+\frac{6802 \log (3+5 x)}{831875}\\ \end{align*}
Mathematica [A] time = 0.0249633, size = 45, normalized size = 0.94 \[ \frac{-\frac{55 \left (490050 x^3+343035 x^2-117076 x-87883\right )}{(5 x+3)^2}-1500625 \log (1-2 x)+27208 \log (10 x+6)}{3327500} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 39, normalized size = 0.8 \begin{align*} -{\frac{81\,x}{250}}-{\frac{2401\,\ln \left ( 2\,x-1 \right ) }{5324}}-{\frac{1}{13750\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{134}{226875+378125\,x}}+{\frac{6802\,\ln \left ( 3+5\,x \right ) }{831875}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0595, size = 53, normalized size = 1.1 \begin{align*} -\frac{81}{250} \, x - \frac{268 \, x + 163}{30250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{6802}{831875} \, \log \left (5 \, x + 3\right ) - \frac{2401}{5324} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.37052, size = 224, normalized size = 4.67 \begin{align*} -\frac{26952750 \, x^{3} + 32343300 \, x^{2} - 27208 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 1500625 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 9732470 \, x + 17930}{3327500 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.16193, size = 39, normalized size = 0.81 \begin{align*} - \frac{81 x}{250} - \frac{268 x + 163}{756250 x^{2} + 907500 x + 272250} - \frac{2401 \log{\left (x - \frac{1}{2} \right )}}{5324} + \frac{6802 \log{\left (x + \frac{3}{5} \right )}}{831875} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.23831, size = 49, normalized size = 1.02 \begin{align*} -\frac{81}{250} \, x - \frac{268 \, x + 163}{30250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{6802}{831875} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{2401}{5324} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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