Optimal. Leaf size=30 \[ -\frac {a^2}{7 x^7}-\frac {a b}{3 x^6}-\frac {b^2}{5 x^5} \]
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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 = {43} \begin {gather*} -\frac {a^2}{7 x^7}-\frac {a b}{3 x^6}-\frac {b^2}{5 x^5} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^2}{x^8} \, dx &=\int \left (\frac {a^2}{x^8}+\frac {2 a b}{x^7}+\frac {b^2}{x^6}\right ) \, dx\\ &=-\frac {a^2}{7 x^7}-\frac {a b}{3 x^6}-\frac {b^2}{5 x^5}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 30, normalized size = 1.00 \begin {gather*} -\frac {a^2}{7 x^7}-\frac {a b}{3 x^6}-\frac {b^2}{5 x^5} \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)^2}{x^8} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.36, size = 24, normalized size = 0.80 \begin {gather*} -\frac {21 \, b^{2} x^{2} + 35 \, a b x + 15 \, a^{2}}{105 \, x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.20, size = 24, normalized size = 0.80 \begin {gather*} -\frac {21 \, b^{2} x^{2} + 35 \, a b x + 15 \, a^{2}}{105 \, x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 25, normalized size = 0.83 \begin {gather*} -\frac {b^{2}}{5 x^{5}}-\frac {a b}{3 x^{6}}-\frac {a^{2}}{7 x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 24, normalized size = 0.80 \begin {gather*} -\frac {21 \, b^{2} x^{2} + 35 \, a b x + 15 \, a^{2}}{105 \, x^{7}} \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}{7}+\frac {a\,b\,x}{3}+\frac {b^2\,x^2}{5}}{x^7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 26, normalized size = 0.87 \begin {gather*} \frac {- 15 a^{2} - 35 a b x - 21 b^{2} x^{2}}{105 x^{7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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