Optimal. Leaf size=69 \[ \frac {a^5 x^{10}}{10}+\frac {5}{12} a^4 b x^{12}+\frac {5}{7} a^3 b^2 x^{14}+\frac {5}{8} a^2 b^3 x^{16}+\frac {5}{18} a b^4 x^{18}+\frac {b^5 x^{20}}{20} \]
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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} \begin {gather*} \frac {5}{8} a^2 b^3 x^{16}+\frac {5}{7} a^3 b^2 x^{14}+\frac {5}{12} a^4 b x^{12}+\frac {a^5 x^{10}}{10}+\frac {5}{18} a b^4 x^{18}+\frac {b^5 x^{20}}{20} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int x^9 \left (a+b x^2\right )^5 \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int x^4 (a+b x)^5 \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {Subst}\left (\int \left (a^5 x^4+5 a^4 b x^5+10 a^3 b^2 x^6+10 a^2 b^3 x^7+5 a b^4 x^8+b^5 x^9\right ) \, dx,x,x^2\right )\\ &=\frac {a^5 x^{10}}{10}+\frac {5}{12} a^4 b x^{12}+\frac {5}{7} a^3 b^2 x^{14}+\frac {5}{8} a^2 b^3 x^{16}+\frac {5}{18} a b^4 x^{18}+\frac {b^5 x^{20}}{20}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 69, normalized size = 1.00 \begin {gather*} \frac {a^5 x^{10}}{10}+\frac {5}{12} a^4 b x^{12}+\frac {5}{7} a^3 b^2 x^{14}+\frac {5}{8} a^2 b^3 x^{16}+\frac {5}{18} a b^4 x^{18}+\frac {b^5 x^{20}}{20} \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^9 \left (a+b x^2\right )^5 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.92, size = 57, normalized size = 0.83 \begin {gather*} \frac {1}{20} x^{20} b^{5} + \frac {5}{18} x^{18} b^{4} a + \frac {5}{8} x^{16} b^{3} a^{2} + \frac {5}{7} x^{14} b^{2} a^{3} + \frac {5}{12} x^{12} b a^{4} + \frac {1}{10} x^{10} a^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.16, size = 57, normalized size = 0.83 \begin {gather*} \frac {1}{20} \, b^{5} x^{20} + \frac {5}{18} \, a b^{4} x^{18} + \frac {5}{8} \, a^{2} b^{3} x^{16} + \frac {5}{7} \, a^{3} b^{2} x^{14} + \frac {5}{12} \, a^{4} b x^{12} + \frac {1}{10} \, a^{5} x^{10} \end {gather*}
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 \begin {gather*} \frac {1}{20} b^{5} x^{20}+\frac {5}{18} a \,b^{4} x^{18}+\frac {5}{8} a^{2} b^{3} x^{16}+\frac {5}{7} a^{3} b^{2} x^{14}+\frac {5}{12} a^{4} b \,x^{12}+\frac {1}{10} a^{5} x^{10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.37, size = 57, normalized size = 0.83 \begin {gather*} \frac {1}{20} \, b^{5} x^{20} + \frac {5}{18} \, a b^{4} x^{18} + \frac {5}{8} \, a^{2} b^{3} x^{16} + \frac {5}{7} \, a^{3} b^{2} x^{14} + \frac {5}{12} \, a^{4} b x^{12} + \frac {1}{10} \, a^{5} x^{10} \end {gather*}
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 \begin {gather*} \frac {a^5\,x^{10}}{10}+\frac {5\,a^4\,b\,x^{12}}{12}+\frac {5\,a^3\,b^2\,x^{14}}{7}+\frac {5\,a^2\,b^3\,x^{16}}{8}+\frac {5\,a\,b^4\,x^{18}}{18}+\frac {b^5\,x^{20}}{20} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 66, normalized size = 0.96 \begin {gather*} \frac {a^{5} x^{10}}{10} + \frac {5 a^{4} b x^{12}}{12} + \frac {5 a^{3} b^{2} x^{14}}{7} + \frac {5 a^{2} b^{3} x^{16}}{8} + \frac {5 a b^{4} x^{18}}{18} + \frac {b^{5} x^{20}}{20} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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