Optimal. Leaf size=17 \[ -\frac {a}{9 x^9}-\frac {b}{8 x^8} \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {43} \begin {gather*} -\frac {a}{9 x^9}-\frac {b}{8 x^8} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {a+b x}{x^{10}} \, dx &=\int \left (\frac {a}{x^{10}}+\frac {b}{x^9}\right ) \, dx\\ &=-\frac {a}{9 x^9}-\frac {b}{8 x^8}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} -\frac {a}{9 x^9}-\frac {b}{8 x^8} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {a+b x}{x^{10}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.83, size = 13, normalized size = 0.76 \begin {gather*} -\frac {9 \, b x + 8 \, a}{72 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.00, size = 13, normalized size = 0.76 \begin {gather*} -\frac {9 \, b x + 8 \, a}{72 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.82 \begin {gather*} -\frac {b}{8 x^{8}}-\frac {a}{9 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 13, normalized size = 0.76 \begin {gather*} -\frac {9 \, b x + 8 \, a}{72 \, x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 13, normalized size = 0.76 \begin {gather*} -\frac {8\,a+9\,b\,x}{72\,x^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 14, normalized size = 0.82 \begin {gather*} \frac {- 8 a - 9 b x}{72 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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