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 = 0.02, 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} \[ -\frac {81 x}{250}-\frac {134}{75625 (5 x+3)}-\frac {1}{13750 (5 x+3)^2}-\frac {2401 \log (1-2 x)}{5324}+\frac {6802 \log (5 x+3)}{831875} \]
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*}
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Mathematica [A] time = 0.04, 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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fricas [A] time = 1.06, size = 65, normalized size = 1.35 \[ -\frac {26952750 \, x^{3} + 32343300 \, x^{2} - 27208 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 1500625 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 9732470 \, x + 17930}{3327500 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.96, size = 36, normalized size = 0.75 \[ -\frac {81}{250} \, x - \frac {268 \, x + 163}{30250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {6802}{831875} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {2401}{5324} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
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 \[ -\frac {81 x}{250}-\frac {2401 \ln \left (2 x -1\right )}{5324}+\frac {6802 \ln \left (5 x +3\right )}{831875}-\frac {1}{13750 \left (5 x +3\right )^{2}}-\frac {134}{75625 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 39, normalized size = 0.81 \[ -\frac {81}{250} \, x - \frac {268 \, x + 163}{30250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {6802}{831875} \, \log \left (5 \, x + 3\right ) - \frac {2401}{5324} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 33, normalized size = 0.69 \[ \frac {6802\,\ln \left (x+\frac {3}{5}\right )}{831875}-\frac {2401\,\ln \left (x-\frac {1}{2}\right )}{5324}-\frac {81\,x}{250}-\frac {\frac {134\,x}{378125}+\frac {163}{756250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 39, normalized size = 0.81 \[ - \frac {81 x}{250} - \frac {268 x + 163}{756250 x^{2} + 907500 x + 272250} - \frac {2401 \log {\left (x - \frac {1}{2} \right )}}{5324} + \frac {6802 \log {\left (x + \frac {3}{5} \right )}}{831875} \]
Verification of antiderivative is not currently implemented for this CAS.
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