Optimal. Leaf size=54 \[ -1000 x^9-\frac{3675 x^8}{2}+\frac{230 x^7}{7}+\frac{3617 x^6}{2}+\frac{3279 x^5}{5}-\frac{2659 x^4}{4}-375 x^3+108 x^2+108 x \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0225201, antiderivative size = 54, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ -1000 x^9-\frac{3675 x^8}{2}+\frac{230 x^7}{7}+\frac{3617 x^6}{2}+\frac{3279 x^5}{5}-\frac{2659 x^4}{4}-375 x^3+108 x^2+108 x \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin{align*} \int (1-2 x)^3 (2+3 x)^2 (3+5 x)^3 \, dx &=\int \left (108+216 x-1125 x^2-2659 x^3+3279 x^4+10851 x^5+230 x^6-14700 x^7-9000 x^8\right ) \, dx\\ &=108 x+108 x^2-375 x^3-\frac{2659 x^4}{4}+\frac{3279 x^5}{5}+\frac{3617 x^6}{2}+\frac{230 x^7}{7}-\frac{3675 x^8}{2}-1000 x^9\\ \end{align*}
Mathematica [A] time = 0.0022065, size = 54, normalized size = 1. \[ -1000 x^9-\frac{3675 x^8}{2}+\frac{230 x^7}{7}+\frac{3617 x^6}{2}+\frac{3279 x^5}{5}-\frac{2659 x^4}{4}-375 x^3+108 x^2+108 x \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0., size = 45, normalized size = 0.8 \begin{align*} 108\,x+108\,{x}^{2}-375\,{x}^{3}-{\frac{2659\,{x}^{4}}{4}}+{\frac{3279\,{x}^{5}}{5}}+{\frac{3617\,{x}^{6}}{2}}+{\frac{230\,{x}^{7}}{7}}-{\frac{3675\,{x}^{8}}{2}}-1000\,{x}^{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.21777, size = 59, normalized size = 1.09 \begin{align*} -1000 \, x^{9} - \frac{3675}{2} \, x^{8} + \frac{230}{7} \, x^{7} + \frac{3617}{2} \, x^{6} + \frac{3279}{5} \, x^{5} - \frac{2659}{4} \, x^{4} - 375 \, x^{3} + 108 \, x^{2} + 108 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.04753, size = 139, normalized size = 2.57 \begin{align*} -1000 x^{9} - \frac{3675}{2} x^{8} + \frac{230}{7} x^{7} + \frac{3617}{2} x^{6} + \frac{3279}{5} x^{5} - \frac{2659}{4} x^{4} - 375 x^{3} + 108 x^{2} + 108 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.06642, size = 51, normalized size = 0.94 \begin{align*} - 1000 x^{9} - \frac{3675 x^{8}}{2} + \frac{230 x^{7}}{7} + \frac{3617 x^{6}}{2} + \frac{3279 x^{5}}{5} - \frac{2659 x^{4}}{4} - 375 x^{3} + 108 x^{2} + 108 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 2.8249, size = 59, normalized size = 1.09 \begin{align*} -1000 \, x^{9} - \frac{3675}{2} \, x^{8} + \frac{230}{7} \, x^{7} + \frac{3617}{2} \, x^{6} + \frac{3279}{5} \, x^{5} - \frac{2659}{4} \, x^{4} - 375 \, x^{3} + 108 \, x^{2} + 108 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]