Optimal. Leaf size=51 \[ \frac {41223 x}{15625}-\frac {26241 x^2}{6250}-\frac {5003 x^3}{1875}+\frac {2313 x^4}{250}+\frac {108 x^5}{125}-\frac {36 x^6}{5}+\frac {1331 \log (3+5 x)}{78125} \]
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Rubi [A]
time = 0.01, antiderivative size = 51, 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 {36 x^6}{5}+\frac {108 x^5}{125}+\frac {2313 x^4}{250}-\frac {5003 x^3}{1875}-\frac {26241 x^2}{6250}+\frac {41223 x}{15625}+\frac {1331 \log (5 x+3)}{78125} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (2+3 x)^3}{3+5 x} \, dx &=\int \left (\frac {41223}{15625}-\frac {26241 x}{3125}-\frac {5003 x^2}{625}+\frac {4626 x^3}{125}+\frac {108 x^4}{25}-\frac {216 x^5}{5}+\frac {1331}{15625 (3+5 x)}\right ) \, dx\\ &=\frac {41223 x}{15625}-\frac {26241 x^2}{6250}-\frac {5003 x^3}{1875}+\frac {2313 x^4}{250}+\frac {108 x^5}{125}-\frac {36 x^6}{5}+\frac {1331 \log (3+5 x)}{78125}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 42, normalized size = 0.82 \begin {gather*} \frac {4036284+6183450 x-9840375 x^2-6253750 x^3+21684375 x^4+2025000 x^5-16875000 x^6+39930 \log (3+5 x)}{2343750} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 38, normalized size = 0.75
method | result | size |
default | \(\frac {41223 x}{15625}-\frac {26241 x^{2}}{6250}-\frac {5003 x^{3}}{1875}+\frac {2313 x^{4}}{250}+\frac {108 x^{5}}{125}-\frac {36 x^{6}}{5}+\frac {1331 \ln \left (3+5 x \right )}{78125}\) | \(38\) |
norman | \(\frac {41223 x}{15625}-\frac {26241 x^{2}}{6250}-\frac {5003 x^{3}}{1875}+\frac {2313 x^{4}}{250}+\frac {108 x^{5}}{125}-\frac {36 x^{6}}{5}+\frac {1331 \ln \left (3+5 x \right )}{78125}\) | \(38\) |
risch | \(\frac {41223 x}{15625}-\frac {26241 x^{2}}{6250}-\frac {5003 x^{3}}{1875}+\frac {2313 x^{4}}{250}+\frac {108 x^{5}}{125}-\frac {36 x^{6}}{5}+\frac {1331 \ln \left (3+5 x \right )}{78125}\) | \(38\) |
meijerg | \(\frac {1331 \ln \left (1+\frac {5 x}{3}\right )}{78125}-\frac {12 x}{5}+\frac {33 x \left (-5 x +6\right )}{25}+\frac {213 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{500}-\frac {891 x \left (-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{6250}-\frac {729 x \left (\frac {2500}{27} x^{4}-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{15625}+\frac {4374 x \left (-\frac {218750}{243} x^{5}+\frac {17500}{27} x^{4}-\frac {4375}{9} x^{3}+\frac {3500}{9} x^{2}-350 x +420\right )}{546875}\) | \(103\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 37, normalized size = 0.73 \begin {gather*} -\frac {36}{5} \, x^{6} + \frac {108}{125} \, x^{5} + \frac {2313}{250} \, x^{4} - \frac {5003}{1875} \, x^{3} - \frac {26241}{6250} \, x^{2} + \frac {41223}{15625} \, x + \frac {1331}{78125} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.45, size = 37, normalized size = 0.73 \begin {gather*} -\frac {36}{5} \, x^{6} + \frac {108}{125} \, x^{5} + \frac {2313}{250} \, x^{4} - \frac {5003}{1875} \, x^{3} - \frac {26241}{6250} \, x^{2} + \frac {41223}{15625} \, x + \frac {1331}{78125} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 48, normalized size = 0.94 \begin {gather*} - \frac {36 x^{6}}{5} + \frac {108 x^{5}}{125} + \frac {2313 x^{4}}{250} - \frac {5003 x^{3}}{1875} - \frac {26241 x^{2}}{6250} + \frac {41223 x}{15625} + \frac {1331 \log {\left (5 x + 3 \right )}}{78125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.60, size = 38, normalized size = 0.75 \begin {gather*} -\frac {36}{5} \, x^{6} + \frac {108}{125} \, x^{5} + \frac {2313}{250} \, x^{4} - \frac {5003}{1875} \, x^{3} - \frac {26241}{6250} \, x^{2} + \frac {41223}{15625} \, x + \frac {1331}{78125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 35, normalized size = 0.69 \begin {gather*} \frac {41223\,x}{15625}+\frac {1331\,\ln \left (x+\frac {3}{5}\right )}{78125}-\frac {26241\,x^2}{6250}-\frac {5003\,x^3}{1875}+\frac {2313\,x^4}{250}+\frac {108\,x^5}{125}-\frac {36\,x^6}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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