Optimal. Leaf size=41 \[ -\frac {8 x^3}{25}+\frac {122 x^2}{125}-\frac {1098 x}{625}-\frac {1331}{3125 (5 x+3)}+\frac {3267 \log (5 x+3)}{3125} \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 41, 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 = {77} \begin {gather*} -\frac {8 x^3}{25}+\frac {122 x^2}{125}-\frac {1098 x}{625}-\frac {1331}{3125 (5 x+3)}+\frac {3267 \log (5 x+3)}{3125} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (2+3 x)}{(3+5 x)^2} \, dx &=\int \left (-\frac {1098}{625}+\frac {244 x}{125}-\frac {24 x^2}{25}+\frac {1331}{625 (3+5 x)^2}+\frac {3267}{625 (3+5 x)}\right ) \, dx\\ &=-\frac {1098 x}{625}+\frac {122 x^2}{125}-\frac {8 x^3}{25}-\frac {1331}{3125 (3+5 x)}+\frac {3267 \log (3+5 x)}{3125}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 44, normalized size = 1.07 \begin {gather*} \frac {-10000 x^4+24500 x^3-36600 x^2-11865 x+6534 (5 x+3) \log (10 x+6)+9983}{6250 (5 x+3)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1-2 x)^3 (2+3 x)}{(3+5 x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.35, size = 42, normalized size = 1.02 \begin {gather*} -\frac {5000 \, x^{4} - 12250 \, x^{3} + 18300 \, x^{2} - 3267 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 16470 \, x + 1331}{3125 \, {\left (5 \, x + 3\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.88, size = 57, normalized size = 1.39 \begin {gather*} \frac {2}{3125} \, {\left (5 \, x + 3\right )}^{3} {\left (\frac {97}{5 \, x + 3} - \frac {1023}{{\left (5 \, x + 3\right )}^{2}} - 4\right )} - \frac {1331}{3125 \, {\left (5 \, x + 3\right )}} - \frac {3267}{3125} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 32, normalized size = 0.78 \begin {gather*} -\frac {8 x^{3}}{25}+\frac {122 x^{2}}{125}-\frac {1098 x}{625}+\frac {3267 \ln \left (5 x +3\right )}{3125}-\frac {1331}{3125 \left (5 x +3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.54, size = 31, normalized size = 0.76 \begin {gather*} -\frac {8}{25} \, x^{3} + \frac {122}{125} \, x^{2} - \frac {1098}{625} \, x - \frac {1331}{3125 \, {\left (5 \, x + 3\right )}} + \frac {3267}{3125} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 29, normalized size = 0.71 \begin {gather*} \frac {3267\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {1098\,x}{625}-\frac {1331}{15625\,\left (x+\frac {3}{5}\right )}+\frac {122\,x^2}{125}-\frac {8\,x^3}{25} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 34, normalized size = 0.83 \begin {gather*} - \frac {8 x^{3}}{25} + \frac {122 x^{2}}{125} - \frac {1098 x}{625} + \frac {3267 \log {\left (5 x + 3 \right )}}{3125} - \frac {1331}{15625 x + 9375} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________