Optimal. Leaf size=30 \[ -\frac {a^2}{9 x^9}-\frac {a b}{4 x^8}-\frac {b^2}{7 x^7} \]
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Rubi [A]
time = 0.01, antiderivative size = 30, 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^2}{9 x^9}-\frac {a b}{4 x^8}-\frac {b^2}{7 x^7} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int \frac {(a+b x)^2}{x^{10}} \, dx &=\int \left (\frac {a^2}{x^{10}}+\frac {2 a b}{x^9}+\frac {b^2}{x^8}\right ) \, dx\\ &=-\frac {a^2}{9 x^9}-\frac {a b}{4 x^8}-\frac {b^2}{7 x^7}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} -\frac {a^2}{9 x^9}-\frac {a b}{4 x^8}-\frac {b^2}{7 x^7} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 25, normalized size = 0.83
method | result | size |
norman | \(\frac {-\frac {1}{7} x^{2} b^{2}-\frac {1}{4} a b x -\frac {1}{9} a^{2}}{x^{9}}\) | \(24\) |
risch | \(\frac {-\frac {1}{7} x^{2} b^{2}-\frac {1}{4} a b x -\frac {1}{9} a^{2}}{x^{9}}\) | \(24\) |
gosper | \(-\frac {36 x^{2} b^{2}+63 a b x +28 a^{2}}{252 x^{9}}\) | \(25\) |
default | \(-\frac {a^{2}}{9 x^{9}}-\frac {a b}{4 x^{8}}-\frac {b^{2}}{7 x^{7}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 24, normalized size = 0.80 \begin {gather*} -\frac {36 \, b^{2} x^{2} + 63 \, a b x + 28 \, a^{2}}{252 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.71, size = 24, normalized size = 0.80 \begin {gather*} -\frac {36 \, b^{2} x^{2} + 63 \, a b x + 28 \, a^{2}}{252 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 26, normalized size = 0.87 \begin {gather*} \frac {- 28 a^{2} - 63 a b x - 36 b^{2} x^{2}}{252 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.19, size = 24, normalized size = 0.80 \begin {gather*} -\frac {36 \, b^{2} x^{2} + 63 \, a b x + 28 \, a^{2}}{252 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 24, normalized size = 0.80 \begin {gather*} -\frac {\frac {a^2}{9}+\frac {a\,b\,x}{4}+\frac {b^2\,x^2}{7}}{x^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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