Optimal. Leaf size=30 \[ -\frac {a^2}{5 x^5}-\frac {a b}{2 x^4}-\frac {b^2}{3 x^3} \]
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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}{5 x^5}-\frac {a b}{2 x^4}-\frac {b^2}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^2}{x^6} \, dx &=\int \left (\frac {a^2}{x^6}+\frac {2 a b}{x^5}+\frac {b^2}{x^4}\right ) \, dx\\ &=-\frac {a^2}{5 x^5}-\frac {a b}{2 x^4}-\frac {b^2}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 30, normalized size = 1.00 \begin {gather*} -\frac {a^2}{5 x^5}-\frac {a b}{2 x^4}-\frac {b^2}{3 x^3} \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^6} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.43, size = 24, normalized size = 0.80 \begin {gather*} -\frac {10 \, b^{2} x^{2} + 15 \, a b x + 6 \, a^{2}}{30 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.19, size = 24, normalized size = 0.80 \begin {gather*} -\frac {10 \, b^{2} x^{2} + 15 \, a b x + 6 \, a^{2}}{30 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.83 \begin {gather*} -\frac {b^{2}}{3 x^{3}}-\frac {a b}{2 x^{4}}-\frac {a^{2}}{5 x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 24, normalized size = 0.80 \begin {gather*} -\frac {10 \, b^{2} x^{2} + 15 \, a b x + 6 \, a^{2}}{30 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 24, normalized size = 0.80 \begin {gather*} -\frac {\frac {a^2}{5}+\frac {a\,b\,x}{2}+\frac {b^2\,x^2}{3}}{x^5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.19, size = 26, normalized size = 0.87 \begin {gather*} \frac {- 6 a^{2} - 15 a b x - 10 b^{2} x^{2}}{30 x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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