Optimal. Leaf size=69 \[ \frac {a^5 x^6}{6}+\frac {5}{7} a^4 b x^7+\frac {5}{4} a^3 b^2 x^8+\frac {10}{9} a^2 b^3 x^9+\frac {1}{2} a b^4 x^{10}+\frac {b^5 x^{11}}{11} \]
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Rubi [A]
time = 0.03, antiderivative size = 69, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {45}
\begin {gather*} \frac {a^5 x^6}{6}+\frac {5}{7} a^4 b x^7+\frac {5}{4} a^3 b^2 x^8+\frac {10}{9} a^2 b^3 x^9+\frac {1}{2} a b^4 x^{10}+\frac {b^5 x^{11}}{11} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int x^5 (a+b x)^5 \, dx &=\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\\ &=\frac {a^5 x^6}{6}+\frac {5}{7} a^4 b x^7+\frac {5}{4} a^3 b^2 x^8+\frac {10}{9} a^2 b^3 x^9+\frac {1}{2} a b^4 x^{10}+\frac {b^5 x^{11}}{11}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 69, normalized size = 1.00 \begin {gather*} \frac {a^5 x^6}{6}+\frac {5}{7} a^4 b x^7+\frac {5}{4} a^3 b^2 x^8+\frac {10}{9} a^2 b^3 x^9+\frac {1}{2} a b^4 x^{10}+\frac {b^5 x^{11}}{11} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 58, normalized size = 0.84
method | result | size |
gosper | \(\frac {1}{6} a^{5} x^{6}+\frac {5}{7} a^{4} b \,x^{7}+\frac {5}{4} a^{3} b^{2} x^{8}+\frac {10}{9} a^{2} b^{3} x^{9}+\frac {1}{2} a \,b^{4} x^{10}+\frac {1}{11} b^{5} x^{11}\) | \(58\) |
default | \(\frac {1}{6} a^{5} x^{6}+\frac {5}{7} a^{4} b \,x^{7}+\frac {5}{4} a^{3} b^{2} x^{8}+\frac {10}{9} a^{2} b^{3} x^{9}+\frac {1}{2} a \,b^{4} x^{10}+\frac {1}{11} b^{5} x^{11}\) | \(58\) |
norman | \(\frac {1}{6} a^{5} x^{6}+\frac {5}{7} a^{4} b \,x^{7}+\frac {5}{4} a^{3} b^{2} x^{8}+\frac {10}{9} a^{2} b^{3} x^{9}+\frac {1}{2} a \,b^{4} x^{10}+\frac {1}{11} b^{5} x^{11}\) | \(58\) |
risch | \(\frac {1}{6} a^{5} x^{6}+\frac {5}{7} a^{4} b \,x^{7}+\frac {5}{4} a^{3} b^{2} x^{8}+\frac {10}{9} a^{2} b^{3} x^{9}+\frac {1}{2} a \,b^{4} x^{10}+\frac {1}{11} b^{5} x^{11}\) | \(58\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 57, normalized size = 0.83 \begin {gather*} \frac {1}{11} \, b^{5} x^{11} + \frac {1}{2} \, a b^{4} x^{10} + \frac {10}{9} \, a^{2} b^{3} x^{9} + \frac {5}{4} \, a^{3} b^{2} x^{8} + \frac {5}{7} \, a^{4} b x^{7} + \frac {1}{6} \, a^{5} x^{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.01, size = 57, normalized size = 0.83 \begin {gather*} \frac {1}{11} \, b^{5} x^{11} + \frac {1}{2} \, a b^{4} x^{10} + \frac {10}{9} \, a^{2} b^{3} x^{9} + \frac {5}{4} \, a^{3} b^{2} x^{8} + \frac {5}{7} \, a^{4} b x^{7} + \frac {1}{6} \, a^{5} x^{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 65, normalized size = 0.94 \begin {gather*} \frac {a^{5} x^{6}}{6} + \frac {5 a^{4} b x^{7}}{7} + \frac {5 a^{3} b^{2} x^{8}}{4} + \frac {10 a^{2} b^{3} x^{9}}{9} + \frac {a b^{4} x^{10}}{2} + \frac {b^{5} x^{11}}{11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.54, size = 57, normalized size = 0.83 \begin {gather*} \frac {1}{11} \, b^{5} x^{11} + \frac {1}{2} \, a b^{4} x^{10} + \frac {10}{9} \, a^{2} b^{3} x^{9} + \frac {5}{4} \, a^{3} b^{2} x^{8} + \frac {5}{7} \, a^{4} b x^{7} + \frac {1}{6} \, a^{5} x^{6} \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^6}{6}+\frac {5\,a^4\,b\,x^7}{7}+\frac {5\,a^3\,b^2\,x^8}{4}+\frac {10\,a^2\,b^3\,x^9}{9}+\frac {a\,b^4\,x^{10}}{2}+\frac {b^5\,x^{11}}{11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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