Optimal. Leaf size=45 \[ -\frac{25}{486} (3 x+2)^{12}+\frac{65}{297} (3 x+2)^{11}-\frac{4}{45} (3 x+2)^{10}+\frac{7}{729} (3 x+2)^9 \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0308512, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{25}{486} (3 x+2)^{12}+\frac{65}{297} (3 x+2)^{11}-\frac{4}{45} (3 x+2)^{10}+\frac{7}{729} (3 x+2)^9 \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin{align*} \int (1-2 x) (2+3 x)^8 (3+5 x)^2 \, dx &=\int \left (\frac{7}{27} (2+3 x)^8-\frac{8}{3} (2+3 x)^9+\frac{65}{9} (2+3 x)^{10}-\frac{50}{27} (2+3 x)^{11}\right ) \, dx\\ &=\frac{7}{729} (2+3 x)^9-\frac{4}{45} (2+3 x)^{10}+\frac{65}{297} (2+3 x)^{11}-\frac{25}{486} (2+3 x)^{12}\\ \end{align*}
Mathematica [A] time = 0.0025995, size = 69, normalized size = 1.53 \[ -\frac{54675 x^{12}}{2}-\frac{1979235 x^{11}}{11}-\frac{2614194 x^{10}}{5}-869103 x^9-881442 x^8-507600 x^7-71904 x^6+\frac{679008 x^5}{5}+127168 x^4+\frac{173056 x^3}{3}+15360 x^2+2304 x \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 60, normalized size = 1.3 \begin{align*} -{\frac{54675\,{x}^{12}}{2}}-{\frac{1979235\,{x}^{11}}{11}}-{\frac{2614194\,{x}^{10}}{5}}-869103\,{x}^{9}-881442\,{x}^{8}-507600\,{x}^{7}-71904\,{x}^{6}+{\frac{679008\,{x}^{5}}{5}}+127168\,{x}^{4}+{\frac{173056\,{x}^{3}}{3}}+15360\,{x}^{2}+2304\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.15128, size = 80, normalized size = 1.78 \begin{align*} -\frac{54675}{2} \, x^{12} - \frac{1979235}{11} \, x^{11} - \frac{2614194}{5} \, x^{10} - 869103 \, x^{9} - 881442 \, x^{8} - 507600 \, x^{7} - 71904 \, x^{6} + \frac{679008}{5} \, x^{5} + 127168 \, x^{4} + \frac{173056}{3} \, x^{3} + 15360 \, x^{2} + 2304 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.34552, size = 223, normalized size = 4.96 \begin{align*} -\frac{54675}{2} x^{12} - \frac{1979235}{11} x^{11} - \frac{2614194}{5} x^{10} - 869103 x^{9} - 881442 x^{8} - 507600 x^{7} - 71904 x^{6} + \frac{679008}{5} x^{5} + 127168 x^{4} + \frac{173056}{3} x^{3} + 15360 x^{2} + 2304 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.071487, size = 66, normalized size = 1.47 \begin{align*} - \frac{54675 x^{12}}{2} - \frac{1979235 x^{11}}{11} - \frac{2614194 x^{10}}{5} - 869103 x^{9} - 881442 x^{8} - 507600 x^{7} - 71904 x^{6} + \frac{679008 x^{5}}{5} + 127168 x^{4} + \frac{173056 x^{3}}{3} + 15360 x^{2} + 2304 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.75778, size = 80, normalized size = 1.78 \begin{align*} -\frac{54675}{2} \, x^{12} - \frac{1979235}{11} \, x^{11} - \frac{2614194}{5} \, x^{10} - 869103 \, x^{9} - 881442 \, x^{8} - 507600 \, x^{7} - 71904 \, x^{6} + \frac{679008}{5} \, x^{5} + 127168 \, x^{4} + \frac{173056}{3} \, x^{3} + 15360 \, x^{2} + 2304 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]