Optimal. Leaf size=69 \[ -\frac {a^5}{10 x^{10}}-\frac {5 a^4 b}{9 x^9}-\frac {5 a^3 b^2}{4 x^8}-\frac {10 a^2 b^3}{7 x^7}-\frac {5 a b^4}{6 x^6}-\frac {b^5}{5 x^5} \]
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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 = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {45}
\begin {gather*} -\frac {a^5}{10 x^{10}}-\frac {5 a^4 b}{9 x^9}-\frac {5 a^3 b^2}{4 x^8}-\frac {10 a^2 b^3}{7 x^7}-\frac {5 a b^4}{6 x^6}-\frac {b^5}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int \frac {(a+b x)^5}{x^{11}} \, dx &=\int \left (\frac {a^5}{x^{11}}+\frac {5 a^4 b}{x^{10}}+\frac {10 a^3 b^2}{x^9}+\frac {10 a^2 b^3}{x^8}+\frac {5 a b^4}{x^7}+\frac {b^5}{x^6}\right ) \, dx\\ &=-\frac {a^5}{10 x^{10}}-\frac {5 a^4 b}{9 x^9}-\frac {5 a^3 b^2}{4 x^8}-\frac {10 a^2 b^3}{7 x^7}-\frac {5 a b^4}{6 x^6}-\frac {b^5}{5 x^5}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 69, normalized size = 1.00 \begin {gather*} -\frac {a^5}{10 x^{10}}-\frac {5 a^4 b}{9 x^9}-\frac {5 a^3 b^2}{4 x^8}-\frac {10 a^2 b^3}{7 x^7}-\frac {5 a b^4}{6 x^6}-\frac {b^5}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 58, normalized size = 0.84
method | result | size |
norman | \(\frac {-\frac {1}{5} b^{5} x^{5}-\frac {5}{6} a \,b^{4} x^{4}-\frac {10}{7} a^{2} b^{3} x^{3}-\frac {5}{4} a^{3} b^{2} x^{2}-\frac {5}{9} a^{4} b x -\frac {1}{10} a^{5}}{x^{10}}\) | \(57\) |
risch | \(\frac {-\frac {1}{5} b^{5} x^{5}-\frac {5}{6} a \,b^{4} x^{4}-\frac {10}{7} a^{2} b^{3} x^{3}-\frac {5}{4} a^{3} b^{2} x^{2}-\frac {5}{9} a^{4} b x -\frac {1}{10} a^{5}}{x^{10}}\) | \(57\) |
gosper | \(-\frac {252 b^{5} x^{5}+1050 a \,b^{4} x^{4}+1800 a^{2} b^{3} x^{3}+1575 a^{3} b^{2} x^{2}+700 a^{4} b x +126 a^{5}}{1260 x^{10}}\) | \(58\) |
default | \(-\frac {a^{5}}{10 x^{10}}-\frac {5 a^{4} b}{9 x^{9}}-\frac {5 a^{3} b^{2}}{4 x^{8}}-\frac {10 a^{2} b^{3}}{7 x^{7}}-\frac {5 a \,b^{4}}{6 x^{6}}-\frac {b^{5}}{5 x^{5}}\) | \(58\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 57, normalized size = 0.83 \begin {gather*} -\frac {252 \, b^{5} x^{5} + 1050 \, a b^{4} x^{4} + 1800 \, a^{2} b^{3} x^{3} + 1575 \, a^{3} b^{2} x^{2} + 700 \, a^{4} b x + 126 \, a^{5}}{1260 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.75, size = 57, normalized size = 0.83 \begin {gather*} -\frac {252 \, b^{5} x^{5} + 1050 \, a b^{4} x^{4} + 1800 \, a^{2} b^{3} x^{3} + 1575 \, a^{3} b^{2} x^{2} + 700 \, a^{4} b x + 126 \, a^{5}}{1260 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.19, size = 61, normalized size = 0.88 \begin {gather*} \frac {- 126 a^{5} - 700 a^{4} b x - 1575 a^{3} b^{2} x^{2} - 1800 a^{2} b^{3} x^{3} - 1050 a b^{4} x^{4} - 252 b^{5} x^{5}}{1260 x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.13, size = 57, normalized size = 0.83 \begin {gather*} -\frac {252 \, b^{5} x^{5} + 1050 \, a b^{4} x^{4} + 1800 \, a^{2} b^{3} x^{3} + 1575 \, a^{3} b^{2} x^{2} + 700 \, a^{4} b x + 126 \, a^{5}}{1260 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 57, normalized size = 0.83 \begin {gather*} -\frac {\frac {a^5}{10}+\frac {5\,a^4\,b\,x}{9}+\frac {5\,a^3\,b^2\,x^2}{4}+\frac {10\,a^2\,b^3\,x^3}{7}+\frac {5\,a\,b^4\,x^4}{6}+\frac {b^5\,x^5}{5}}{x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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