Optimal. Leaf size=37 \[ -\frac {27 x}{625}-\frac {183 x^2}{125}+\frac {172 x^3}{75}-\frac {6 x^4}{5}+\frac {1331 \log (3+5 x)}{3125} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} -\frac {6 x^4}{5}+\frac {172 x^3}{75}-\frac {183 x^2}{125}-\frac {27 x}{625}+\frac {1331 \log (5 x+3)}{3125} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 78
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (2+3 x)}{3+5 x} \, dx &=\int \left (-\frac {27}{625}-\frac {366 x}{125}+\frac {172 x^2}{25}-\frac {24 x^3}{5}+\frac {1331}{625 (3+5 x)}\right ) \, dx\\ &=-\frac {27 x}{625}-\frac {183 x^2}{125}+\frac {172 x^3}{75}-\frac {6 x^4}{5}+\frac {1331 \log (3+5 x)}{3125}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 35, normalized size = 0.95 \begin {gather*} \frac {-5 \left (-2160+81 x+2745 x^2-4300 x^3+2250 x^4\right )+3993 \log (3+5 x)}{9375} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.08, size = 28, normalized size = 0.76
method | result | size |
default | \(-\frac {27 x}{625}-\frac {183 x^{2}}{125}+\frac {172 x^{3}}{75}-\frac {6 x^{4}}{5}+\frac {1331 \ln \left (3+5 x \right )}{3125}\) | \(28\) |
norman | \(-\frac {27 x}{625}-\frac {183 x^{2}}{125}+\frac {172 x^{3}}{75}-\frac {6 x^{4}}{5}+\frac {1331 \ln \left (3+5 x \right )}{3125}\) | \(28\) |
risch | \(-\frac {27 x}{625}-\frac {183 x^{2}}{125}+\frac {172 x^{3}}{75}-\frac {6 x^{4}}{5}+\frac {1331 \ln \left (3+5 x \right )}{3125}\) | \(28\) |
meijerg | \(\frac {1331 \ln \left (1+\frac {5 x}{3}\right )}{3125}-\frac {9 x}{5}-\frac {3 x \left (-5 x +6\right )}{25}+\frac {3 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{25}+\frac {54 x \left (-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{3125}\) | \(52\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 27, normalized size = 0.73 \begin {gather*} -\frac {6}{5} \, x^{4} + \frac {172}{75} \, x^{3} - \frac {183}{125} \, x^{2} - \frac {27}{625} \, x + \frac {1331}{3125} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.41, size = 27, normalized size = 0.73 \begin {gather*} -\frac {6}{5} \, x^{4} + \frac {172}{75} \, x^{3} - \frac {183}{125} \, x^{2} - \frac {27}{625} \, x + \frac {1331}{3125} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.03, size = 34, normalized size = 0.92 \begin {gather*} - \frac {6 x^{4}}{5} + \frac {172 x^{3}}{75} - \frac {183 x^{2}}{125} - \frac {27 x}{625} + \frac {1331 \log {\left (5 x + 3 \right )}}{3125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.56, size = 28, normalized size = 0.76 \begin {gather*} -\frac {6}{5} \, x^{4} + \frac {172}{75} \, x^{3} - \frac {183}{125} \, x^{2} - \frac {27}{625} \, x + \frac {1331}{3125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.02, size = 25, normalized size = 0.68 \begin {gather*} \frac {1331\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {27\,x}{625}-\frac {183\,x^2}{125}+\frac {172\,x^3}{75}-\frac {6\,x^4}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________