Optimal. Leaf size=51 \[ -\frac {36 x^6}{5}+\frac {108 x^5}{125}+\frac {2313 x^4}{250}-\frac {5003 x^3}{1875}-\frac {26241 x^2}{6250}+\frac {41223 x}{15625}+\frac {1331 \log (5 x+3)}{78125} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, 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 = {88} \[ -\frac {36 x^6}{5}+\frac {108 x^5}{125}+\frac {2313 x^4}{250}-\frac {5003 x^3}{1875}-\frac {26241 x^2}{6250}+\frac {41223 x}{15625}+\frac {1331 \log (5 x+3)}{78125} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
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*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 42, normalized size = 0.82 \[ \frac {-16875000 x^6+2025000 x^5+21684375 x^4-6253750 x^3-9840375 x^2+6183450 x+39930 \log (5 x+3)+4036284}{2343750} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.52, size = 37, normalized size = 0.73 \[ -\frac {36}{5} \, x^{6} + \frac {108}{125} \, x^{5} + \frac {2313}{250} \, x^{4} - \frac {5003}{1875} \, x^{3} - \frac {26241}{6250} \, x^{2} + \frac {41223}{15625} \, x + \frac {1331}{78125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.08, size = 38, normalized size = 0.75 \[ -\frac {36}{5} \, x^{6} + \frac {108}{125} \, x^{5} + \frac {2313}{250} \, x^{4} - \frac {5003}{1875} \, x^{3} - \frac {26241}{6250} \, x^{2} + \frac {41223}{15625} \, x + \frac {1331}{78125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 38, normalized size = 0.75 \[ -\frac {36 x^{6}}{5}+\frac {108 x^{5}}{125}+\frac {2313 x^{4}}{250}-\frac {5003 x^{3}}{1875}-\frac {26241 x^{2}}{6250}+\frac {41223 x}{15625}+\frac {1331 \ln \left (5 x +3\right )}{78125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.50, size = 37, normalized size = 0.73 \[ -\frac {36}{5} \, x^{6} + \frac {108}{125} \, x^{5} + \frac {2313}{250} \, x^{4} - \frac {5003}{1875} \, x^{3} - \frac {26241}{6250} \, x^{2} + \frac {41223}{15625} \, x + \frac {1331}{78125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 35, normalized size = 0.69 \[ \frac {41223\,x}{15625}+\frac {1331\,\ln \left (x+\frac {3}{5}\right )}{78125}-\frac {26241\,x^2}{6250}-\frac {5003\,x^3}{1875}+\frac {2313\,x^4}{250}+\frac {108\,x^5}{125}-\frac {36\,x^6}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 48, normalized size = 0.94 \[ - \frac {36 x^{6}}{5} + \frac {108 x^{5}}{125} + \frac {2313 x^{4}}{250} - \frac {5003 x^{3}}{1875} - \frac {26241 x^{2}}{6250} + \frac {41223 x}{15625} + \frac {1331 \log {\left (5 x + 3 \right )}}{78125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________