Optimal. Leaf size=43 \[ -\frac {a^3}{6 x^6}-\frac {3 a^2 b}{5 x^5}-\frac {3 a b^2}{4 x^4}-\frac {b^3}{3 x^3} \]
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Rubi [A] time = 0.01, antiderivative size = 43, 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 {3 a^2 b}{5 x^5}-\frac {a^3}{6 x^6}-\frac {3 a b^2}{4 x^4}-\frac {b^3}{3 x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^3}{x^7} \, dx &=\int \left (\frac {a^3}{x^7}+\frac {3 a^2 b}{x^6}+\frac {3 a b^2}{x^5}+\frac {b^3}{x^4}\right ) \, dx\\ &=-\frac {a^3}{6 x^6}-\frac {3 a^2 b}{5 x^5}-\frac {3 a b^2}{4 x^4}-\frac {b^3}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 43, normalized size = 1.00 \begin {gather*} -\frac {a^3}{6 x^6}-\frac {3 a^2 b}{5 x^5}-\frac {3 a b^2}{4 x^4}-\frac {b^3}{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)^3}{x^7} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.97, size = 35, normalized size = 0.81 \begin {gather*} -\frac {20 \, b^{3} x^{3} + 45 \, a b^{2} x^{2} + 36 \, a^{2} b x + 10 \, a^{3}}{60 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.15, size = 35, normalized size = 0.81 \begin {gather*} -\frac {20 \, b^{3} x^{3} + 45 \, a b^{2} x^{2} + 36 \, a^{2} b x + 10 \, a^{3}}{60 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 36, normalized size = 0.84 \begin {gather*} -\frac {b^{3}}{3 x^{3}}-\frac {3 a \,b^{2}}{4 x^{4}}-\frac {3 a^{2} b}{5 x^{5}}-\frac {a^{3}}{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 = 35, normalized size = 0.81 \begin {gather*} -\frac {20 \, b^{3} x^{3} + 45 \, a b^{2} x^{2} + 36 \, a^{2} b x + 10 \, a^{3}}{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 = 35, normalized size = 0.81 \begin {gather*} -\frac {\frac {a^3}{6}+\frac {3\,a^2\,b\,x}{5}+\frac {3\,a\,b^2\,x^2}{4}+\frac {b^3\,x^3}{3}}{x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.34, size = 37, normalized size = 0.86 \begin {gather*} \frac {- 10 a^{3} - 36 a^{2} b x - 45 a b^{2} x^{2} - 20 b^{3} x^{3}}{60 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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