Optimal. Leaf size=66 \[ \frac {a^5 x^3}{3}+a^4 b x^5+\frac {10}{7} a^3 b^2 x^7+\frac {10}{9} a^2 b^3 x^9+\frac {5}{11} a b^4 x^{11}+\frac {b^5 x^{13}}{13} \]
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Rubi [A] time = 0.02, antiderivative size = 66, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {270} \[ \frac {10}{9} a^2 b^3 x^9+\frac {10}{7} a^3 b^2 x^7+a^4 b x^5+\frac {a^5 x^3}{3}+\frac {5}{11} a b^4 x^{11}+\frac {b^5 x^{13}}{13} \]
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int x^2 \left (a+b x^2\right )^5 \, dx &=\int \left (a^5 x^2+5 a^4 b x^4+10 a^3 b^2 x^6+10 a^2 b^3 x^8+5 a b^4 x^{10}+b^5 x^{12}\right ) \, dx\\ &=\frac {a^5 x^3}{3}+a^4 b x^5+\frac {10}{7} a^3 b^2 x^7+\frac {10}{9} a^2 b^3 x^9+\frac {5}{11} a b^4 x^{11}+\frac {b^5 x^{13}}{13}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 66, normalized size = 1.00 \[ \frac {a^5 x^3}{3}+a^4 b x^5+\frac {10}{7} a^3 b^2 x^7+\frac {10}{9} a^2 b^3 x^9+\frac {5}{11} a b^4 x^{11}+\frac {b^5 x^{13}}{13} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 56, normalized size = 0.85 \[ \frac {1}{13} x^{13} b^{5} + \frac {5}{11} x^{11} b^{4} a + \frac {10}{9} x^{9} b^{3} a^{2} + \frac {10}{7} x^{7} b^{2} a^{3} + x^{5} b a^{4} + \frac {1}{3} x^{3} a^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.09, size = 56, normalized size = 0.85 \[ \frac {1}{13} \, b^{5} x^{13} + \frac {5}{11} \, a b^{4} x^{11} + \frac {10}{9} \, a^{2} b^{3} x^{9} + \frac {10}{7} \, a^{3} b^{2} x^{7} + a^{4} b x^{5} + \frac {1}{3} \, a^{5} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 57, normalized size = 0.86 \[ \frac {1}{13} b^{5} x^{13}+\frac {5}{11} a \,b^{4} x^{11}+\frac {10}{9} a^{2} b^{3} x^{9}+\frac {10}{7} a^{3} b^{2} x^{7}+a^{4} b \,x^{5}+\frac {1}{3} a^{5} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.38, size = 56, normalized size = 0.85 \[ \frac {1}{13} \, b^{5} x^{13} + \frac {5}{11} \, a b^{4} x^{11} + \frac {10}{9} \, a^{2} b^{3} x^{9} + \frac {10}{7} \, a^{3} b^{2} x^{7} + a^{4} b x^{5} + \frac {1}{3} \, a^{5} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 56, normalized size = 0.85 \[ \frac {a^5\,x^3}{3}+a^4\,b\,x^5+\frac {10\,a^3\,b^2\,x^7}{7}+\frac {10\,a^2\,b^3\,x^9}{9}+\frac {5\,a\,b^4\,x^{11}}{11}+\frac {b^5\,x^{13}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 63, normalized size = 0.95 \[ \frac {a^{5} x^{3}}{3} + a^{4} b x^{5} + \frac {10 a^{3} b^{2} x^{7}}{7} + \frac {10 a^{2} b^{3} x^{9}}{9} + \frac {5 a b^{4} x^{11}}{11} + \frac {b^{5} x^{13}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
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