Optimal. Leaf size=33 \[ \frac {332 x}{225}-\frac {4 x^2}{15}-\frac {343}{27} \log (2+3 x)+\frac {1331}{125} \log (3+5 x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 33, 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 = {84}
\begin {gather*} -\frac {4 x^2}{15}+\frac {332 x}{225}-\frac {343}{27} \log (3 x+2)+\frac {1331}{125} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 84
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3}{(2+3 x) (3+5 x)} \, dx &=\int \left (\frac {332}{225}-\frac {8 x}{15}-\frac {343}{9 (2+3 x)}+\frac {1331}{25 (3+5 x)}\right ) \, dx\\ &=\frac {332 x}{225}-\frac {4 x^2}{15}-\frac {343}{27} \log (2+3 x)+\frac {1331}{125} \log (3+5 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 35, normalized size = 1.06 \begin {gather*} \frac {60 \left (62+83 x-15 x^2\right )-42875 \log (2+3 x)+35937 \log (-3 (3+5 x))}{3375} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.11, size = 26, normalized size = 0.79
method | result | size |
default | \(\frac {332 x}{225}-\frac {4 x^{2}}{15}-\frac {343 \ln \left (2+3 x \right )}{27}+\frac {1331 \ln \left (3+5 x \right )}{125}\) | \(26\) |
norman | \(\frac {332 x}{225}-\frac {4 x^{2}}{15}-\frac {343 \ln \left (2+3 x \right )}{27}+\frac {1331 \ln \left (3+5 x \right )}{125}\) | \(26\) |
risch | \(\frac {332 x}{225}-\frac {4 x^{2}}{15}-\frac {343 \ln \left (2+3 x \right )}{27}+\frac {1331 \ln \left (3+5 x \right )}{125}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 25, normalized size = 0.76 \begin {gather*} -\frac {4}{15} \, x^{2} + \frac {332}{225} \, x + \frac {1331}{125} \, \log \left (5 \, x + 3\right ) - \frac {343}{27} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.44, size = 25, normalized size = 0.76 \begin {gather*} -\frac {4}{15} \, x^{2} + \frac {332}{225} \, x + \frac {1331}{125} \, \log \left (5 \, x + 3\right ) - \frac {343}{27} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.04, size = 31, normalized size = 0.94 \begin {gather*} - \frac {4 x^{2}}{15} + \frac {332 x}{225} + \frac {1331 \log {\left (x + \frac {3}{5} \right )}}{125} - \frac {343 \log {\left (x + \frac {2}{3} \right )}}{27} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.53, size = 27, normalized size = 0.82 \begin {gather*} -\frac {4}{15} \, x^{2} + \frac {332}{225} \, x + \frac {1331}{125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {343}{27} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 21, normalized size = 0.64 \begin {gather*} \frac {332\,x}{225}-\frac {343\,\ln \left (x+\frac {2}{3}\right )}{27}+\frac {1331\,\ln \left (x+\frac {3}{5}\right )}{125}-\frac {4\,x^2}{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________