Optimal. Leaf size=56 \[ -\frac {a^4}{9 x^9}-\frac {a^3 b}{2 x^8}-\frac {6 a^2 b^2}{7 x^7}-\frac {2 a b^3}{3 x^6}-\frac {b^4}{5 x^5} \]
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Rubi [A]
time = 0.01, antiderivative size = 56, 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^4}{9 x^9}-\frac {a^3 b}{2 x^8}-\frac {6 a^2 b^2}{7 x^7}-\frac {2 a b^3}{3 x^6}-\frac {b^4}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int \frac {(a+b x)^4}{x^{10}} \, dx &=\int \left (\frac {a^4}{x^{10}}+\frac {4 a^3 b}{x^9}+\frac {6 a^2 b^2}{x^8}+\frac {4 a b^3}{x^7}+\frac {b^4}{x^6}\right ) \, dx\\ &=-\frac {a^4}{9 x^9}-\frac {a^3 b}{2 x^8}-\frac {6 a^2 b^2}{7 x^7}-\frac {2 a b^3}{3 x^6}-\frac {b^4}{5 x^5}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 56, normalized size = 1.00 \begin {gather*} -\frac {a^4}{9 x^9}-\frac {a^3 b}{2 x^8}-\frac {6 a^2 b^2}{7 x^7}-\frac {2 a b^3}{3 x^6}-\frac {b^4}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 47, normalized size = 0.84
method | result | size |
norman | \(\frac {-\frac {1}{5} b^{4} x^{4}-\frac {2}{3} a \,b^{3} x^{3}-\frac {6}{7} a^{2} b^{2} x^{2}-\frac {1}{2} a^{3} b x -\frac {1}{9} a^{4}}{x^{9}}\) | \(46\) |
risch | \(\frac {-\frac {1}{5} b^{4} x^{4}-\frac {2}{3} a \,b^{3} x^{3}-\frac {6}{7} a^{2} b^{2} x^{2}-\frac {1}{2} a^{3} b x -\frac {1}{9} a^{4}}{x^{9}}\) | \(46\) |
gosper | \(-\frac {126 b^{4} x^{4}+420 a \,b^{3} x^{3}+540 a^{2} b^{2} x^{2}+315 a^{3} b x +70 a^{4}}{630 x^{9}}\) | \(47\) |
default | \(-\frac {a^{4}}{9 x^{9}}-\frac {a^{3} b}{2 x^{8}}-\frac {6 a^{2} b^{2}}{7 x^{7}}-\frac {2 a \,b^{3}}{3 x^{6}}-\frac {b^{4}}{5 x^{5}}\) | \(47\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 46, normalized size = 0.82 \begin {gather*} -\frac {126 \, b^{4} x^{4} + 420 \, a b^{3} x^{3} + 540 \, a^{2} b^{2} x^{2} + 315 \, a^{3} b x + 70 \, a^{4}}{630 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 46, normalized size = 0.82 \begin {gather*} -\frac {126 \, b^{4} x^{4} + 420 \, a b^{3} x^{3} + 540 \, a^{2} b^{2} x^{2} + 315 \, a^{3} b x + 70 \, a^{4}}{630 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.16, size = 49, normalized size = 0.88 \begin {gather*} \frac {- 70 a^{4} - 315 a^{3} b x - 540 a^{2} b^{2} x^{2} - 420 a b^{3} x^{3} - 126 b^{4} x^{4}}{630 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.20, size = 46, normalized size = 0.82 \begin {gather*} -\frac {126 \, b^{4} x^{4} + 420 \, a b^{3} x^{3} + 540 \, a^{2} b^{2} x^{2} + 315 \, a^{3} b x + 70 \, a^{4}}{630 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 46, normalized size = 0.82 \begin {gather*} -\frac {\frac {a^4}{9}+\frac {a^3\,b\,x}{2}+\frac {6\,a^2\,b^2\,x^2}{7}+\frac {2\,a\,b^3\,x^3}{3}+\frac {b^4\,x^4}{5}}{x^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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