Optimal. Leaf size=41 \[ -\frac {18 x^3}{25}-\frac {81 x^2}{250}+\frac {522 x}{625}-\frac {11}{3125 (5 x+3)}+\frac {97 \log (5 x+3)}{3125} \]
[Out]
________________________________________________________________________________________
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} \[ -\frac {18 x^3}{25}-\frac {81 x^2}{250}+\frac {522 x}{625}-\frac {11}{3125 (5 x+3)}+\frac {97 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int \frac {(1-2 x) (2+3 x)^3}{(3+5 x)^2} \, dx &=\int \left (\frac {522}{625}-\frac {81 x}{125}-\frac {54 x^2}{25}+\frac {11}{625 (3+5 x)^2}+\frac {97}{625 (3+5 x)}\right ) \, dx\\ &=\frac {522 x}{625}-\frac {81 x^2}{250}-\frac {18 x^3}{25}-\frac {11}{3125 (3+5 x)}+\frac {97 \log (3+5 x)}{3125}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 46, normalized size = 1.12 \[ \frac {-67500 x^4-70875 x^3+60075 x^2+92680 x+582 (5 x+3) \log (-3 (5 x+3))+27354}{18750 (5 x+3)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.55, size = 42, normalized size = 1.02 \[ -\frac {22500 \, x^{4} + 23625 \, x^{3} - 20025 \, x^{2} - 194 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 15660 \, x + 22}{6250 \, {\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.15, size = 57, normalized size = 1.39 \[ \frac {9}{6250} \, {\left (5 \, x + 3\right )}^{3} {\left (\frac {27}{5 \, x + 3} + \frac {62}{{\left (5 \, x + 3\right )}^{2}} - 4\right )} - \frac {11}{3125 \, {\left (5 \, x + 3\right )}} - \frac {97}{3125} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 32, normalized size = 0.78 \[ -\frac {18 x^{3}}{25}-\frac {81 x^{2}}{250}+\frac {522 x}{625}+\frac {97 \ln \left (5 x +3\right )}{3125}-\frac {11}{3125 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.63, size = 31, normalized size = 0.76 \[ -\frac {18}{25} \, x^{3} - \frac {81}{250} \, x^{2} + \frac {522}{625} \, x - \frac {11}{3125 \, {\left (5 \, x + 3\right )}} + \frac {97}{3125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 29, normalized size = 0.71 \[ \frac {522\,x}{625}+\frac {97\,\ln \left (x+\frac {3}{5}\right )}{3125}-\frac {11}{15625\,\left (x+\frac {3}{5}\right )}-\frac {81\,x^2}{250}-\frac {18\,x^3}{25} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 34, normalized size = 0.83 \[ - \frac {18 x^{3}}{25} - \frac {81 x^{2}}{250} + \frac {522 x}{625} + \frac {97 \log {\left (5 x + 3 \right )}}{3125} - \frac {11}{15625 x + 9375} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________