Optimal. Leaf size=115 \[ \frac {1}{2} a^4 A x^2+\frac {1}{3} a^4 B x^3+a^3 A c x^4+\frac {4}{5} a^3 B c x^5+a^2 A c^2 x^6+\frac {6}{7} a^2 B c^2 x^7+\frac {1}{2} a A c^3 x^8+\frac {4}{9} a B c^3 x^9+\frac {1}{10} A c^4 x^{10}+\frac {1}{11} B c^4 x^{11} \]
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Rubi [A] time = 0.12, antiderivative size = 115, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {766} \begin {gather*} a^2 A c^2 x^6+a^3 A c x^4+\frac {1}{2} a^4 A x^2+\frac {6}{7} a^2 B c^2 x^7+\frac {4}{5} a^3 B c x^5+\frac {1}{3} a^4 B x^3+\frac {1}{2} a A c^3 x^8+\frac {4}{9} a B c^3 x^9+\frac {1}{10} A c^4 x^{10}+\frac {1}{11} B c^4 x^{11} \end {gather*}
Antiderivative was successfully verified.
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Rule 766
Rubi steps
\begin {align*} \int x (A+B x) \left (a+c x^2\right )^4 \, dx &=\int \left (a^4 A x+a^4 B x^2+4 a^3 A c x^3+4 a^3 B c x^4+6 a^2 A c^2 x^5+6 a^2 B c^2 x^6+4 a A c^3 x^7+4 a B c^3 x^8+A c^4 x^9+B c^4 x^{10}\right ) \, dx\\ &=\frac {1}{2} a^4 A x^2+\frac {1}{3} a^4 B x^3+a^3 A c x^4+\frac {4}{5} a^3 B c x^5+a^2 A c^2 x^6+\frac {6}{7} a^2 B c^2 x^7+\frac {1}{2} a A c^3 x^8+\frac {4}{9} a B c^3 x^9+\frac {1}{10} A c^4 x^{10}+\frac {1}{11} B c^4 x^{11}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 115, normalized size = 1.00 \begin {gather*} \frac {1}{2} a^4 A x^2+\frac {1}{3} a^4 B x^3+a^3 A c x^4+\frac {4}{5} a^3 B c x^5+a^2 A c^2 x^6+\frac {6}{7} a^2 B c^2 x^7+\frac {1}{2} a A c^3 x^8+\frac {4}{9} a B c^3 x^9+\frac {1}{10} A c^4 x^{10}+\frac {1}{11} B c^4 x^{11} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x (A+B x) \left (a+c x^2\right )^4 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.36, size = 99, normalized size = 0.86 \begin {gather*} \frac {1}{11} x^{11} c^{4} B + \frac {1}{10} x^{10} c^{4} A + \frac {4}{9} x^{9} c^{3} a B + \frac {1}{2} x^{8} c^{3} a A + \frac {6}{7} x^{7} c^{2} a^{2} B + x^{6} c^{2} a^{2} A + \frac {4}{5} x^{5} c a^{3} B + x^{4} c a^{3} A + \frac {1}{3} x^{3} a^{4} B + \frac {1}{2} x^{2} a^{4} A \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 99, normalized size = 0.86 \begin {gather*} \frac {1}{11} \, B c^{4} x^{11} + \frac {1}{10} \, A c^{4} x^{10} + \frac {4}{9} \, B a c^{3} x^{9} + \frac {1}{2} \, A a c^{3} x^{8} + \frac {6}{7} \, B a^{2} c^{2} x^{7} + A a^{2} c^{2} x^{6} + \frac {4}{5} \, B a^{3} c x^{5} + A a^{3} c x^{4} + \frac {1}{3} \, B a^{4} x^{3} + \frac {1}{2} \, A a^{4} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 100, normalized size = 0.87 \begin {gather*} \frac {1}{11} B \,c^{4} x^{11}+\frac {1}{10} A \,c^{4} x^{10}+\frac {4}{9} B a \,c^{3} x^{9}+\frac {1}{2} A a \,c^{3} x^{8}+\frac {6}{7} B \,a^{2} c^{2} x^{7}+A \,a^{2} c^{2} x^{6}+\frac {4}{5} B \,a^{3} c \,x^{5}+A \,a^{3} c \,x^{4}+\frac {1}{3} B \,a^{4} x^{3}+\frac {1}{2} A \,a^{4} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.60, size = 99, normalized size = 0.86 \begin {gather*} \frac {1}{11} \, B c^{4} x^{11} + \frac {1}{10} \, A c^{4} x^{10} + \frac {4}{9} \, B a c^{3} x^{9} + \frac {1}{2} \, A a c^{3} x^{8} + \frac {6}{7} \, B a^{2} c^{2} x^{7} + A a^{2} c^{2} x^{6} + \frac {4}{5} \, B a^{3} c x^{5} + A a^{3} c x^{4} + \frac {1}{3} \, B a^{4} x^{3} + \frac {1}{2} \, A a^{4} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 99, normalized size = 0.86 \begin {gather*} \frac {B\,a^4\,x^3}{3}+\frac {A\,a^4\,x^2}{2}+\frac {4\,B\,a^3\,c\,x^5}{5}+A\,a^3\,c\,x^4+\frac {6\,B\,a^2\,c^2\,x^7}{7}+A\,a^2\,c^2\,x^6+\frac {4\,B\,a\,c^3\,x^9}{9}+\frac {A\,a\,c^3\,x^8}{2}+\frac {B\,c^4\,x^{11}}{11}+\frac {A\,c^4\,x^{10}}{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 116, normalized size = 1.01 \begin {gather*} \frac {A a^{4} x^{2}}{2} + A a^{3} c x^{4} + A a^{2} c^{2} x^{6} + \frac {A a c^{3} x^{8}}{2} + \frac {A c^{4} x^{10}}{10} + \frac {B a^{4} x^{3}}{3} + \frac {4 B a^{3} c x^{5}}{5} + \frac {6 B a^{2} c^{2} x^{7}}{7} + \frac {4 B a c^{3} x^{9}}{9} + \frac {B c^{4} x^{11}}{11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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