Optimal. Leaf size=69 \[ \frac {a^5 x^{12}}{12}+\frac {5}{14} a^4 b x^{14}+\frac {5}{8} a^3 b^2 x^{16}+\frac {5}{9} a^2 b^3 x^{18}+\frac {1}{4} a b^4 x^{20}+\frac {b^5 x^{22}}{22} \]
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Rubi [A] time = 0.04, antiderivative size = 69, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac {5}{9} a^2 b^3 x^{18}+\frac {5}{8} a^3 b^2 x^{16}+\frac {5}{14} a^4 b x^{14}+\frac {a^5 x^{12}}{12}+\frac {1}{4} a b^4 x^{20}+\frac {b^5 x^{22}}{22} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int x^{11} \left (a+b x^2\right )^5 \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int x^5 (a+b x)^5 \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (a^5 x^5+5 a^4 b x^6+10 a^3 b^2 x^7+10 a^2 b^3 x^8+5 a b^4 x^9+b^5 x^{10}\right ) \, dx,x,x^2\right )\\ &=\frac {a^5 x^{12}}{12}+\frac {5}{14} a^4 b x^{14}+\frac {5}{8} a^3 b^2 x^{16}+\frac {5}{9} a^2 b^3 x^{18}+\frac {1}{4} a b^4 x^{20}+\frac {b^5 x^{22}}{22}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 69, normalized size = 1.00 \[ \frac {a^5 x^{12}}{12}+\frac {5}{14} a^4 b x^{14}+\frac {5}{8} a^3 b^2 x^{16}+\frac {5}{9} a^2 b^3 x^{18}+\frac {1}{4} a b^4 x^{20}+\frac {b^5 x^{22}}{22} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 57, normalized size = 0.83 \[ \frac {1}{22} x^{22} b^{5} + \frac {1}{4} x^{20} b^{4} a + \frac {5}{9} x^{18} b^{3} a^{2} + \frac {5}{8} x^{16} b^{2} a^{3} + \frac {5}{14} x^{14} b a^{4} + \frac {1}{12} x^{12} a^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.01, size = 57, normalized size = 0.83 \[ \frac {1}{22} \, b^{5} x^{22} + \frac {1}{4} \, a b^{4} x^{20} + \frac {5}{9} \, a^{2} b^{3} x^{18} + \frac {5}{8} \, a^{3} b^{2} x^{16} + \frac {5}{14} \, a^{4} b x^{14} + \frac {1}{12} \, a^{5} x^{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 58, normalized size = 0.84 \[ \frac {1}{22} b^{5} x^{22}+\frac {1}{4} a \,b^{4} x^{20}+\frac {5}{9} a^{2} b^{3} x^{18}+\frac {5}{8} a^{3} b^{2} x^{16}+\frac {5}{14} a^{4} b \,x^{14}+\frac {1}{12} a^{5} x^{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.36, size = 57, normalized size = 0.83 \[ \frac {1}{22} \, b^{5} x^{22} + \frac {1}{4} \, a b^{4} x^{20} + \frac {5}{9} \, a^{2} b^{3} x^{18} + \frac {5}{8} \, a^{3} b^{2} x^{16} + \frac {5}{14} \, a^{4} b x^{14} + \frac {1}{12} \, a^{5} x^{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 57, normalized size = 0.83 \[ \frac {a^5\,x^{12}}{12}+\frac {5\,a^4\,b\,x^{14}}{14}+\frac {5\,a^3\,b^2\,x^{16}}{8}+\frac {5\,a^2\,b^3\,x^{18}}{9}+\frac {a\,b^4\,x^{20}}{4}+\frac {b^5\,x^{22}}{22} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 65, normalized size = 0.94 \[ \frac {a^{5} x^{12}}{12} + \frac {5 a^{4} b x^{14}}{14} + \frac {5 a^{3} b^{2} x^{16}}{8} + \frac {5 a^{2} b^{3} x^{18}}{9} + \frac {a b^{4} x^{20}}{4} + \frac {b^{5} x^{22}}{22} \]
Verification of antiderivative is not currently implemented for this CAS.
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