Optimal. Leaf size=56 \[ -\frac{10}{729} (3 x+2)^{12}+\frac{428 (3 x+2)^{11}}{2673}-\frac{259}{405} (3 x+2)^{10}+\frac{2009 (3 x+2)^9}{2187}-\frac{343 (3 x+2)^8}{1944} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0285949, antiderivative size = 56, 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} \[ -\frac{10}{729} (3 x+2)^{12}+\frac{428 (3 x+2)^{11}}{2673}-\frac{259}{405} (3 x+2)^{10}+\frac{2009 (3 x+2)^9}{2187}-\frac{343 (3 x+2)^8}{1944} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin{align*} \int (1-2 x)^3 (2+3 x)^7 (3+5 x) \, dx &=\int \left (-\frac{343}{81} (2+3 x)^7+\frac{2009}{81} (2+3 x)^8-\frac{518}{27} (2+3 x)^9+\frac{428}{81} (2+3 x)^{10}-\frac{40}{81} (2+3 x)^{11}\right ) \, dx\\ &=-\frac{343 (2+3 x)^8}{1944}+\frac{2009 (2+3 x)^9}{2187}-\frac{259}{405} (2+3 x)^{10}+\frac{428 (2+3 x)^{11}}{2673}-\frac{10}{729} (2+3 x)^{12}\\ \end{align*}
Mathematica [A] time = 0.0024932, size = 67, normalized size = 1.2 \[ -7290 x^{12}-\frac{329508 x^{11}}{11}-\frac{217971 x^{10}}{5}-15507 x^9+\frac{208035 x^8}{8}+29106 x^7+3514 x^6-\frac{48968 x^5}{5}-5148 x^4+480 x^3+1184 x^2+384 x \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 60, normalized size = 1.1 \begin{align*} -7290\,{x}^{12}-{\frac{329508\,{x}^{11}}{11}}-{\frac{217971\,{x}^{10}}{5}}-15507\,{x}^{9}+{\frac{208035\,{x}^{8}}{8}}+29106\,{x}^{7}+3514\,{x}^{6}-{\frac{48968\,{x}^{5}}{5}}-5148\,{x}^{4}+480\,{x}^{3}+1184\,{x}^{2}+384\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.06409, size = 80, normalized size = 1.43 \begin{align*} -7290 \, x^{12} - \frac{329508}{11} \, x^{11} - \frac{217971}{5} \, x^{10} - 15507 \, x^{9} + \frac{208035}{8} \, x^{8} + 29106 \, x^{7} + 3514 \, x^{6} - \frac{48968}{5} \, x^{5} - 5148 \, x^{4} + 480 \, x^{3} + 1184 \, x^{2} + 384 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.18691, size = 201, normalized size = 3.59 \begin{align*} -7290 x^{12} - \frac{329508}{11} x^{11} - \frac{217971}{5} x^{10} - 15507 x^{9} + \frac{208035}{8} x^{8} + 29106 x^{7} + 3514 x^{6} - \frac{48968}{5} x^{5} - 5148 x^{4} + 480 x^{3} + 1184 x^{2} + 384 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.070811, size = 65, normalized size = 1.16 \begin{align*} - 7290 x^{12} - \frac{329508 x^{11}}{11} - \frac{217971 x^{10}}{5} - 15507 x^{9} + \frac{208035 x^{8}}{8} + 29106 x^{7} + 3514 x^{6} - \frac{48968 x^{5}}{5} - 5148 x^{4} + 480 x^{3} + 1184 x^{2} + 384 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.52882, size = 80, normalized size = 1.43 \begin{align*} -7290 \, x^{12} - \frac{329508}{11} \, x^{11} - \frac{217971}{5} \, x^{10} - 15507 \, x^{9} + \frac{208035}{8} \, x^{8} + 29106 \, x^{7} + 3514 \, x^{6} - \frac{48968}{5} \, x^{5} - 5148 \, x^{4} + 480 \, x^{3} + 1184 \, x^{2} + 384 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]