Optimal. Leaf size=93 \[ \frac {1}{3} a^3 A x^3+\frac {1}{4} a^3 B x^4+\frac {3}{5} a^2 A c x^5+\frac {1}{2} a^2 B c x^6+\frac {3}{7} a A c^2 x^7+\frac {3}{8} a B c^2 x^8+\frac {1}{9} A c^3 x^9+\frac {1}{10} B c^3 x^{10} \]
________________________________________________________________________________________
Rubi [A] time = 0.09, antiderivative size = 93, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {766} \begin {gather*} \frac {3}{5} a^2 A c x^5+\frac {1}{3} a^3 A x^3+\frac {1}{2} a^2 B c x^6+\frac {1}{4} a^3 B x^4+\frac {3}{7} a A c^2 x^7+\frac {3}{8} a B c^2 x^8+\frac {1}{9} A c^3 x^9+\frac {1}{10} B c^3 x^{10} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 766
Rubi steps
\begin {align*} \int x^2 (A+B x) \left (a+c x^2\right )^3 \, dx &=\int \left (a^3 A x^2+a^3 B x^3+3 a^2 A c x^4+3 a^2 B c x^5+3 a A c^2 x^6+3 a B c^2 x^7+A c^3 x^8+B c^3 x^9\right ) \, dx\\ &=\frac {1}{3} a^3 A x^3+\frac {1}{4} a^3 B x^4+\frac {3}{5} a^2 A c x^5+\frac {1}{2} a^2 B c x^6+\frac {3}{7} a A c^2 x^7+\frac {3}{8} a B c^2 x^8+\frac {1}{9} A c^3 x^9+\frac {1}{10} B c^3 x^{10}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 93, normalized size = 1.00 \begin {gather*} \frac {1}{3} a^3 A x^3+\frac {1}{4} a^3 B x^4+\frac {3}{5} a^2 A c x^5+\frac {1}{2} a^2 B c x^6+\frac {3}{7} a A c^2 x^7+\frac {3}{8} a B c^2 x^8+\frac {1}{9} A c^3 x^9+\frac {1}{10} B c^3 x^{10} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^2 (A+B x) \left (a+c x^2\right )^3 \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.35, size = 77, normalized size = 0.83 \begin {gather*} \frac {1}{10} x^{10} c^{3} B + \frac {1}{9} x^{9} c^{3} A + \frac {3}{8} x^{8} c^{2} a B + \frac {3}{7} x^{7} c^{2} a A + \frac {1}{2} x^{6} c a^{2} B + \frac {3}{5} x^{5} c a^{2} A + \frac {1}{4} x^{4} a^{3} B + \frac {1}{3} x^{3} a^{3} A \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 77, normalized size = 0.83 \begin {gather*} \frac {1}{10} \, B c^{3} x^{10} + \frac {1}{9} \, A c^{3} x^{9} + \frac {3}{8} \, B a c^{2} x^{8} + \frac {3}{7} \, A a c^{2} x^{7} + \frac {1}{2} \, B a^{2} c x^{6} + \frac {3}{5} \, A a^{2} c x^{5} + \frac {1}{4} \, B a^{3} x^{4} + \frac {1}{3} \, A a^{3} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 78, normalized size = 0.84 \begin {gather*} \frac {1}{10} B \,c^{3} x^{10}+\frac {1}{9} A \,c^{3} x^{9}+\frac {3}{8} B a \,c^{2} x^{8}+\frac {3}{7} A a \,c^{2} x^{7}+\frac {1}{2} B \,a^{2} c \,x^{6}+\frac {3}{5} A \,a^{2} c \,x^{5}+\frac {1}{4} B \,a^{3} x^{4}+\frac {1}{3} A \,a^{3} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.51, size = 77, normalized size = 0.83 \begin {gather*} \frac {1}{10} \, B c^{3} x^{10} + \frac {1}{9} \, A c^{3} x^{9} + \frac {3}{8} \, B a c^{2} x^{8} + \frac {3}{7} \, A a c^{2} x^{7} + \frac {1}{2} \, B a^{2} c x^{6} + \frac {3}{5} \, A a^{2} c x^{5} + \frac {1}{4} \, B a^{3} x^{4} + \frac {1}{3} \, A a^{3} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 77, normalized size = 0.83 \begin {gather*} \frac {B\,a^3\,x^4}{4}+\frac {A\,a^3\,x^3}{3}+\frac {B\,a^2\,c\,x^6}{2}+\frac {3\,A\,a^2\,c\,x^5}{5}+\frac {3\,B\,a\,c^2\,x^8}{8}+\frac {3\,A\,a\,c^2\,x^7}{7}+\frac {B\,c^3\,x^{10}}{10}+\frac {A\,c^3\,x^9}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 92, normalized size = 0.99 \begin {gather*} \frac {A a^{3} x^{3}}{3} + \frac {3 A a^{2} c x^{5}}{5} + \frac {3 A a c^{2} x^{7}}{7} + \frac {A c^{3} x^{9}}{9} + \frac {B a^{3} x^{4}}{4} + \frac {B a^{2} c x^{6}}{2} + \frac {3 B a c^{2} x^{8}}{8} + \frac {B c^{3} x^{10}}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________