Optimal. Leaf size=48 \[ -\frac {81 x}{250}-\frac {1}{13750 (3+5 x)^2}-\frac {134}{75625 (3+5 x)}-\frac {2401 \log (1-2 x)}{5324}+\frac {6802 \log (3+5 x)}{831875} \]
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Rubi [A]
time = 0.01, 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 = {90}
\begin {gather*} -\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} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
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 = 0.02, size = 45, normalized size = 0.94 \begin {gather*} \frac {-\frac {55 \left (-87883-117076 x+343035 x^2+490050 x^3\right )}{(3+5 x)^2}-1500625 \log (1-2 x)+27208 \log (6+10 x)}{3327500} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 39, normalized size = 0.81
method | result | size |
risch | \(-\frac {81 x}{250}+\frac {-\frac {134 x}{15125}-\frac {163}{30250}}{\left (3+5 x \right )^{2}}-\frac {2401 \ln \left (-1+2 x \right )}{5324}+\frac {6802 \ln \left (3+5 x \right )}{831875}\) | \(35\) |
default | \(-\frac {81 x}{250}-\frac {2401 \ln \left (-1+2 x \right )}{5324}-\frac {1}{13750 \left (3+5 x \right )^{2}}-\frac {134}{75625 \left (3+5 x \right )}+\frac {6802 \ln \left (3+5 x \right )}{831875}\) | \(39\) |
norman | \(\frac {-\frac {263801}{90750} x -\frac {528439}{54450} x^{2}-\frac {81}{10} x^{3}}{\left (3+5 x \right )^{2}}-\frac {2401 \ln \left (-1+2 x \right )}{5324}+\frac {6802 \ln \left (3+5 x \right )}{831875}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.38, size = 39, normalized size = 0.81 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.77, size = 65, normalized size = 1.35 \begin {gather*} -\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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 39, normalized size = 0.81 \begin {gather*} - \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.78, size = 36, normalized size = 0.75 \begin {gather*} -\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 {gather*}
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 \begin {gather*} \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}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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