Optimal. Leaf size=30 \[ -\frac {a^2}{6 x^6}-\frac {2 a b}{5 x^5}-\frac {b^2}{4 x^4} \]
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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}{6 x^6}-\frac {2 a b}{5 x^5}-\frac {b^2}{4 x^4} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^2}{x^7} \, dx &=\int \left (\frac {a^2}{x^7}+\frac {2 a b}{x^6}+\frac {b^2}{x^5}\right ) \, dx\\ &=-\frac {a^2}{6 x^6}-\frac {2 a b}{5 x^5}-\frac {b^2}{4 x^4}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} -\frac {a^2}{6 x^6}-\frac {2 a b}{5 x^5}-\frac {b^2}{4 x^4} \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^7} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.72, size = 24, normalized size = 0.80 \begin {gather*} -\frac {15 \, b^{2} x^{2} + 24 \, a b x + 10 \, a^{2}}{60 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.07, size = 24, normalized size = 0.80 \begin {gather*} -\frac {15 \, b^{2} x^{2} + 24 \, a b x + 10 \, a^{2}}{60 \, x^{6}} \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}}{4 x^{4}}-\frac {2 a b}{5 x^{5}}-\frac {a^{2}}{6 x^{6}} \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 {15 \, b^{2} x^{2} + 24 \, a b x + 10 \, a^{2}}{60 \, x^{6}} \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}{6}+\frac {2\,a\,b\,x}{5}+\frac {b^2\,x^2}{4}}{x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 26, normalized size = 0.87 \begin {gather*} \frac {- 10 a^{2} - 24 a b x - 15 b^{2} x^{2}}{60 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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