Optimal. Leaf size=55 \[ -\frac {4941 x}{2500}-\frac {243 x^2}{500}-\frac {1}{68750 (3+5 x)^2}-\frac {167}{378125 (3+5 x)}-\frac {16807 \log (1-2 x)}{10648}+\frac {11224 \log (3+5 x)}{4159375} \]
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Rubi [A]
time = 0.02, antiderivative size = 55, 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 {243 x^2}{500}-\frac {4941 x}{2500}-\frac {167}{378125 (5 x+3)}-\frac {1}{68750 (5 x+3)^2}-\frac {16807 \log (1-2 x)}{10648}+\frac {11224 \log (5 x+3)}{4159375} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^5}{(1-2 x) (3+5 x)^3} \, dx &=\int \left (-\frac {4941}{2500}-\frac {243 x}{250}-\frac {16807}{5324 (-1+2 x)}+\frac {1}{6875 (3+5 x)^3}+\frac {167}{75625 (3+5 x)^2}+\frac {11224}{831875 (3+5 x)}\right ) \, dx\\ &=-\frac {4941 x}{2500}-\frac {243 x^2}{500}-\frac {1}{68750 (3+5 x)^2}-\frac {167}{378125 (3+5 x)}-\frac {16807 \log (1-2 x)}{10648}+\frac {11224 \log (3+5 x)}{4159375}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 50, normalized size = 0.91 \begin {gather*} \frac {-\frac {11 \left (-60415061-93782210 x+217337175 x^2+387139500 x^3+73507500 x^4\right )}{(3+5 x)^2}-105043750 \log (1-2 x)+179584 \log (6+10 x)}{66550000} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 44, normalized size = 0.80
method | result | size |
risch | \(-\frac {243 x^{2}}{500}-\frac {4941 x}{2500}+\frac {-\frac {167 x}{75625}-\frac {1013}{756250}}{\left (3+5 x \right )^{2}}-\frac {16807 \ln \left (-1+2 x \right )}{10648}+\frac {11224 \ln \left (3+5 x \right )}{4159375}\) | \(40\) |
default | \(-\frac {243 x^{2}}{500}-\frac {4941 x}{2500}-\frac {16807 \ln \left (-1+2 x \right )}{10648}-\frac {1}{68750 \left (3+5 x \right )^{2}}-\frac {167}{378125 \left (3+5 x \right )}+\frac {11224 \ln \left (3+5 x \right )}{4159375}\) | \(44\) |
norman | \(\frac {-\frac {16140199}{907500} x -\frac {34664111}{544500} x^{2}-\frac {6399}{100} x^{3}-\frac {243}{20} x^{4}}{\left (3+5 x \right )^{2}}-\frac {16807 \ln \left (-1+2 x \right )}{10648}+\frac {11224 \ln \left (3+5 x \right )}{4159375}\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 44, normalized size = 0.80 \begin {gather*} -\frac {243}{500} \, x^{2} - \frac {4941}{2500} \, x - \frac {1670 \, x + 1013}{756250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {11224}{4159375} \, \log \left (5 \, x + 3\right ) - \frac {16807}{10648} \, \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 = 1.01, size = 70, normalized size = 1.27 \begin {gather*} -\frac {404291250 \, x^{4} + 2129267250 \, x^{3} + 2118486150 \, x^{2} - 89792 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 52521875 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 591955870 \, x + 44572}{33275000 \, {\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 = 0.07, size = 46, normalized size = 0.84 \begin {gather*} - \frac {243 x^{2}}{500} - \frac {4941 x}{2500} - \frac {1670 x + 1013}{18906250 x^{2} + 22687500 x + 6806250} - \frac {16807 \log {\left (x - \frac {1}{2} \right )}}{10648} + \frac {11224 \log {\left (x + \frac {3}{5} \right )}}{4159375} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.06, size = 41, normalized size = 0.75 \begin {gather*} -\frac {243}{500} \, x^{2} - \frac {4941}{2500} \, x - \frac {1670 \, x + 1013}{756250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {11224}{4159375} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {16807}{10648} \, \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 = 38, normalized size = 0.69 \begin {gather*} \frac {11224\,\ln \left (x+\frac {3}{5}\right )}{4159375}-\frac {16807\,\ln \left (x-\frac {1}{2}\right )}{10648}-\frac {4941\,x}{2500}-\frac {\frac {167\,x}{1890625}+\frac {1013}{18906250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}-\frac {243\,x^2}{500} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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