Optimal. Leaf size=59 \[ -2700 x^{10}-6900 x^9-\frac {14355 x^8}{4}+\frac {33013 x^7}{7}+\frac {10513 x^6}{2}-\frac {1419 x^5}{5}-\frac {8693 x^4}{4}-534 x^3+378 x^2+216 x \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 59, normalized size of antiderivative = 1.00, 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} \begin {gather*} -2700 x^{10}-6900 x^9-\frac {14355 x^8}{4}+\frac {33013 x^7}{7}+\frac {10513 x^6}{2}-\frac {1419 x^5}{5}-\frac {8693 x^4}{4}-534 x^3+378 x^2+216 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
Rubi steps
\begin {align*} \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^3 \, dx &=\int \left (216+756 x-1602 x^2-8693 x^3-1419 x^4+31539 x^5+33013 x^6-28710 x^7-62100 x^8-27000 x^9\right ) \, dx\\ &=216 x+378 x^2-534 x^3-\frac {8693 x^4}{4}-\frac {1419 x^5}{5}+\frac {10513 x^6}{2}+\frac {33013 x^7}{7}-\frac {14355 x^8}{4}-6900 x^9-2700 x^{10}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 59, normalized size = 1.00 \begin {gather*} -2700 x^{10}-6900 x^9-\frac {14355 x^8}{4}+\frac {33013 x^7}{7}+\frac {10513 x^6}{2}-\frac {1419 x^5}{5}-\frac {8693 x^4}{4}-534 x^3+378 x^2+216 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^3 \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.11, size = 49, normalized size = 0.83 \begin {gather*} -2700 x^{10} - 6900 x^{9} - \frac {14355}{4} x^{8} + \frac {33013}{7} x^{7} + \frac {10513}{2} x^{6} - \frac {1419}{5} x^{5} - \frac {8693}{4} x^{4} - 534 x^{3} + 378 x^{2} + 216 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.77, size = 49, normalized size = 0.83 \begin {gather*} -2700 \, x^{10} - 6900 \, x^{9} - \frac {14355}{4} \, x^{8} + \frac {33013}{7} \, x^{7} + \frac {10513}{2} \, x^{6} - \frac {1419}{5} \, x^{5} - \frac {8693}{4} \, x^{4} - 534 \, x^{3} + 378 \, x^{2} + 216 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 50, normalized size = 0.85 \begin {gather*} -2700 x^{10}-6900 x^{9}-\frac {14355}{4} x^{8}+\frac {33013}{7} x^{7}+\frac {10513}{2} x^{6}-\frac {1419}{5} x^{5}-\frac {8693}{4} x^{4}-534 x^{3}+378 x^{2}+216 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.61, size = 49, normalized size = 0.83 \begin {gather*} -2700 \, x^{10} - 6900 \, x^{9} - \frac {14355}{4} \, x^{8} + \frac {33013}{7} \, x^{7} + \frac {10513}{2} \, x^{6} - \frac {1419}{5} \, x^{5} - \frac {8693}{4} \, x^{4} - 534 \, x^{3} + 378 \, x^{2} + 216 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 49, normalized size = 0.83 \begin {gather*} -2700\,x^{10}-6900\,x^9-\frac {14355\,x^8}{4}+\frac {33013\,x^7}{7}+\frac {10513\,x^6}{2}-\frac {1419\,x^5}{5}-\frac {8693\,x^4}{4}-534\,x^3+378\,x^2+216\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 56, normalized size = 0.95 \begin {gather*} - 2700 x^{10} - 6900 x^{9} - \frac {14355 x^{8}}{4} + \frac {33013 x^{7}}{7} + \frac {10513 x^{6}}{2} - \frac {1419 x^{5}}{5} - \frac {8693 x^{4}}{4} - 534 x^{3} + 378 x^{2} + 216 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________