Optimal. Leaf size=43 \[ -\frac {1}{2750 (3+5 x)^2}-\frac {101}{15125 (3+5 x)}-\frac {343 \log (1-2 x)}{2662}+\frac {3469 \log (3+5 x)}{166375} \]
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Rubi [A]
time = 0.01, antiderivative size = 43, 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 {101}{15125 (5 x+3)}-\frac {1}{2750 (5 x+3)^2}-\frac {343 \log (1-2 x)}{2662}+\frac {3469 \log (5 x+3)}{166375} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^3}{(1-2 x) (3+5 x)^3} \, dx &=\int \left (-\frac {343}{1331 (-1+2 x)}+\frac {1}{275 (3+5 x)^3}+\frac {101}{3025 (3+5 x)^2}+\frac {3469}{33275 (3+5 x)}\right ) \, dx\\ &=-\frac {1}{2750 (3+5 x)^2}-\frac {101}{15125 (3+5 x)}-\frac {343 \log (1-2 x)}{2662}+\frac {3469 \log (3+5 x)}{166375}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 35, normalized size = 0.81 \begin {gather*} \frac {-\frac {11 (617+1010 x)}{(3+5 x)^2}-42875 \log (1-2 x)+6938 \log (6+10 x)}{332750} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 36, normalized size = 0.84
method | result | size |
risch | \(\frac {-\frac {101 x}{3025}-\frac {617}{30250}}{\left (3+5 x \right )^{2}}-\frac {343 \ln \left (-1+2 x \right )}{2662}+\frac {3469 \ln \left (3+5 x \right )}{166375}\) | \(32\) |
norman | \(\frac {\frac {314}{9075} x +\frac {617}{10890} x^{2}}{\left (3+5 x \right )^{2}}-\frac {343 \ln \left (-1+2 x \right )}{2662}+\frac {3469 \ln \left (3+5 x \right )}{166375}\) | \(35\) |
default | \(-\frac {343 \ln \left (-1+2 x \right )}{2662}-\frac {1}{2750 \left (3+5 x \right )^{2}}-\frac {101}{15125 \left (3+5 x \right )}+\frac {3469 \ln \left (3+5 x \right )}{166375}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 36, normalized size = 0.84 \begin {gather*} -\frac {1010 \, x + 617}{30250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {3469}{166375} \, \log \left (5 \, x + 3\right ) - \frac {343}{2662} \, \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 = 55, normalized size = 1.28 \begin {gather*} \frac {6938 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 42875 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (2 \, x - 1\right ) - 11110 \, x - 6787}{332750 \, {\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 = 34, normalized size = 0.79 \begin {gather*} - \frac {1010 x + 617}{756250 x^{2} + 907500 x + 272250} - \frac {343 \log {\left (x - \frac {1}{2} \right )}}{2662} + \frac {3469 \log {\left (x + \frac {3}{5} \right )}}{166375} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.34, size = 33, normalized size = 0.77 \begin {gather*} -\frac {1010 \, x + 617}{30250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {3469}{166375} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {343}{2662} \, \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 = 1.16, size = 30, normalized size = 0.70 \begin {gather*} \frac {3469\,\ln \left (x+\frac {3}{5}\right )}{166375}-\frac {343\,\ln \left (x-\frac {1}{2}\right )}{2662}-\frac {\frac {101\,x}{75625}+\frac {617}{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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