Optimal. Leaf size=69 \[ \frac {a^5 x^5}{5}+\frac {5}{7} a^4 b x^7+\frac {10}{9} a^3 b^2 x^9+\frac {10}{11} a^2 b^3 x^{11}+\frac {5}{13} a b^4 x^{13}+\frac {b^5 x^{15}}{15} \]
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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^5}{5}+\frac {5}{7} a^4 b x^7+\frac {10}{9} a^3 b^2 x^9+\frac {10}{11} a^2 b^3 x^{11}+\frac {5}{13} a b^4 x^{13}+\frac {b^5 x^{15}}{15} \end {gather*}
Antiderivative was successfully verified.
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Rule 276
Rubi steps
\begin {align*} \int x^4 \left (a+b x^2\right )^5 \, dx &=\int \left (a^5 x^4+5 a^4 b x^6+10 a^3 b^2 x^8+10 a^2 b^3 x^{10}+5 a b^4 x^{12}+b^5 x^{14}\right ) \, dx\\ &=\frac {a^5 x^5}{5}+\frac {5}{7} a^4 b x^7+\frac {10}{9} a^3 b^2 x^9+\frac {10}{11} a^2 b^3 x^{11}+\frac {5}{13} a b^4 x^{13}+\frac {b^5 x^{15}}{15}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 69, normalized size = 1.00 \begin {gather*} \frac {a^5 x^5}{5}+\frac {5}{7} a^4 b x^7+\frac {10}{9} a^3 b^2 x^9+\frac {10}{11} a^2 b^3 x^{11}+\frac {5}{13} a b^4 x^{13}+\frac {b^5 x^{15}}{15} \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 | \(\frac {1}{5} a^{5} x^{5}+\frac {5}{7} a^{4} b \,x^{7}+\frac {10}{9} a^{3} b^{2} x^{9}+\frac {10}{11} a^{2} b^{3} x^{11}+\frac {5}{13} a \,b^{4} x^{13}+\frac {1}{15} b^{5} x^{15}\) | \(58\) |
default | \(\frac {1}{5} a^{5} x^{5}+\frac {5}{7} a^{4} b \,x^{7}+\frac {10}{9} a^{3} b^{2} x^{9}+\frac {10}{11} a^{2} b^{3} x^{11}+\frac {5}{13} a \,b^{4} x^{13}+\frac {1}{15} b^{5} x^{15}\) | \(58\) |
norman | \(\frac {1}{5} a^{5} x^{5}+\frac {5}{7} a^{4} b \,x^{7}+\frac {10}{9} a^{3} b^{2} x^{9}+\frac {10}{11} a^{2} b^{3} x^{11}+\frac {5}{13} a \,b^{4} x^{13}+\frac {1}{15} b^{5} x^{15}\) | \(58\) |
risch | \(\frac {1}{5} a^{5} x^{5}+\frac {5}{7} a^{4} b \,x^{7}+\frac {10}{9} a^{3} b^{2} x^{9}+\frac {10}{11} a^{2} b^{3} x^{11}+\frac {5}{13} a \,b^{4} x^{13}+\frac {1}{15} b^{5} x^{15}\) | \(58\) |
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}{15} \, b^{5} x^{15} + \frac {5}{13} \, a b^{4} x^{13} + \frac {10}{11} \, a^{2} b^{3} x^{11} + \frac {10}{9} \, a^{3} b^{2} x^{9} + \frac {5}{7} \, a^{4} b x^{7} + \frac {1}{5} \, a^{5} x^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.71, size = 57, normalized size = 0.83 \begin {gather*} \frac {1}{15} \, b^{5} x^{15} + \frac {5}{13} \, a b^{4} x^{13} + \frac {10}{11} \, a^{2} b^{3} x^{11} + \frac {10}{9} \, a^{3} b^{2} x^{9} + \frac {5}{7} \, a^{4} b x^{7} + \frac {1}{5} \, a^{5} x^{5} \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^{5}}{5} + \frac {5 a^{4} b x^{7}}{7} + \frac {10 a^{3} b^{2} x^{9}}{9} + \frac {10 a^{2} b^{3} x^{11}}{11} + \frac {5 a b^{4} x^{13}}{13} + \frac {b^{5} x^{15}}{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.81, size = 57, normalized size = 0.83 \begin {gather*} \frac {1}{15} \, b^{5} x^{15} + \frac {5}{13} \, a b^{4} x^{13} + \frac {10}{11} \, a^{2} b^{3} x^{11} + \frac {10}{9} \, a^{3} b^{2} x^{9} + \frac {5}{7} \, a^{4} b x^{7} + \frac {1}{5} \, a^{5} x^{5} \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^5}{5}+\frac {5\,a^4\,b\,x^7}{7}+\frac {10\,a^3\,b^2\,x^9}{9}+\frac {10\,a^2\,b^3\,x^{11}}{11}+\frac {5\,a\,b^4\,x^{13}}{13}+\frac {b^5\,x^{15}}{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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