Optimal. Leaf size=69 \[ \frac {a^5 x^9}{9}+\frac {5}{11} a^4 b x^{11}+\frac {10}{13} a^3 b^2 x^{13}+\frac {2}{3} a^2 b^3 x^{15}+\frac {5}{17} a b^4 x^{17}+\frac {b^5 x^{19}}{19} \]
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Rubi [A]
time = 0.02, antiderivative size = 69, 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 = {276}
\begin {gather*} \frac {a^5 x^9}{9}+\frac {5}{11} a^4 b x^{11}+\frac {10}{13} a^3 b^2 x^{13}+\frac {2}{3} a^2 b^3 x^{15}+\frac {5}{17} a b^4 x^{17}+\frac {b^5 x^{19}}{19} \end {gather*}
Antiderivative was successfully verified.
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Rule 276
Rubi steps
\begin {align*} \int x^8 \left (a+b x^2\right )^5 \, dx &=\int \left (a^5 x^8+5 a^4 b x^{10}+10 a^3 b^2 x^{12}+10 a^2 b^3 x^{14}+5 a b^4 x^{16}+b^5 x^{18}\right ) \, dx\\ &=\frac {a^5 x^9}{9}+\frac {5}{11} a^4 b x^{11}+\frac {10}{13} a^3 b^2 x^{13}+\frac {2}{3} a^2 b^3 x^{15}+\frac {5}{17} a b^4 x^{17}+\frac {b^5 x^{19}}{19}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 69, normalized size = 1.00 \begin {gather*} \frac {a^5 x^9}{9}+\frac {5}{11} a^4 b x^{11}+\frac {10}{13} a^3 b^2 x^{13}+\frac {2}{3} a^2 b^3 x^{15}+\frac {5}{17} a b^4 x^{17}+\frac {b^5 x^{19}}{19} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 58, normalized size = 0.84
method | result | size |
gosper | \(\frac {1}{9} a^{5} x^{9}+\frac {5}{11} a^{4} b \,x^{11}+\frac {10}{13} a^{3} b^{2} x^{13}+\frac {2}{3} a^{2} b^{3} x^{15}+\frac {5}{17} a \,b^{4} x^{17}+\frac {1}{19} b^{5} x^{19}\) | \(58\) |
default | \(\frac {1}{9} a^{5} x^{9}+\frac {5}{11} a^{4} b \,x^{11}+\frac {10}{13} a^{3} b^{2} x^{13}+\frac {2}{3} a^{2} b^{3} x^{15}+\frac {5}{17} a \,b^{4} x^{17}+\frac {1}{19} b^{5} x^{19}\) | \(58\) |
norman | \(\frac {1}{9} a^{5} x^{9}+\frac {5}{11} a^{4} b \,x^{11}+\frac {10}{13} a^{3} b^{2} x^{13}+\frac {2}{3} a^{2} b^{3} x^{15}+\frac {5}{17} a \,b^{4} x^{17}+\frac {1}{19} b^{5} x^{19}\) | \(58\) |
risch | \(\frac {1}{9} a^{5} x^{9}+\frac {5}{11} a^{4} b \,x^{11}+\frac {10}{13} a^{3} b^{2} x^{13}+\frac {2}{3} a^{2} b^{3} x^{15}+\frac {5}{17} a \,b^{4} x^{17}+\frac {1}{19} b^{5} x^{19}\) | \(58\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 57, normalized size = 0.83 \begin {gather*} \frac {1}{19} \, b^{5} x^{19} + \frac {5}{17} \, a b^{4} x^{17} + \frac {2}{3} \, a^{2} b^{3} x^{15} + \frac {10}{13} \, a^{3} b^{2} x^{13} + \frac {5}{11} \, a^{4} b x^{11} + \frac {1}{9} \, a^{5} x^{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.98, size = 57, normalized size = 0.83 \begin {gather*} \frac {1}{19} \, b^{5} x^{19} + \frac {5}{17} \, a b^{4} x^{17} + \frac {2}{3} \, a^{2} b^{3} x^{15} + \frac {10}{13} \, a^{3} b^{2} x^{13} + \frac {5}{11} \, a^{4} b x^{11} + \frac {1}{9} \, a^{5} x^{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 66, normalized size = 0.96 \begin {gather*} \frac {a^{5} x^{9}}{9} + \frac {5 a^{4} b x^{11}}{11} + \frac {10 a^{3} b^{2} x^{13}}{13} + \frac {2 a^{2} b^{3} x^{15}}{3} + \frac {5 a b^{4} x^{17}}{17} + \frac {b^{5} x^{19}}{19} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.51, size = 57, normalized size = 0.83 \begin {gather*} \frac {1}{19} \, b^{5} x^{19} + \frac {5}{17} \, a b^{4} x^{17} + \frac {2}{3} \, a^{2} b^{3} x^{15} + \frac {10}{13} \, a^{3} b^{2} x^{13} + \frac {5}{11} \, a^{4} b x^{11} + \frac {1}{9} \, a^{5} x^{9} \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^9}{9}+\frac {5\,a^4\,b\,x^{11}}{11}+\frac {10\,a^3\,b^2\,x^{13}}{13}+\frac {2\,a^2\,b^3\,x^{15}}{3}+\frac {5\,a\,b^4\,x^{17}}{17}+\frac {b^5\,x^{19}}{19} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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