Optimal. Leaf size=43 \[ -\frac {a^3}{3 x^3}-\frac {3 a^2 b}{4 x^4}-\frac {3 a b^2}{5 x^5}-\frac {b^3}{6 x^6} \]
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Rubi [A] time = 0.01, antiderivative size = 43, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {263, 43} \[ -\frac {3 a^2 b}{4 x^4}-\frac {a^3}{3 x^3}-\frac {3 a b^2}{5 x^5}-\frac {b^3}{6 x^6} \]
Antiderivative was successfully verified.
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Rule 43
Rule 263
Rubi steps
\begin {align*} \int \frac {\left (a+\frac {b}{x}\right )^3}{x^4} \, dx &=\int \frac {(b+a x)^3}{x^7} \, dx\\ &=\int \left (\frac {b^3}{x^7}+\frac {3 a b^2}{x^6}+\frac {3 a^2 b}{x^5}+\frac {a^3}{x^4}\right ) \, dx\\ &=-\frac {b^3}{6 x^6}-\frac {3 a b^2}{5 x^5}-\frac {3 a^2 b}{4 x^4}-\frac {a^3}{3 x^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 43, normalized size = 1.00 \[ -\frac {a^3}{3 x^3}-\frac {3 a^2 b}{4 x^4}-\frac {3 a b^2}{5 x^5}-\frac {b^3}{6 x^6} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.00, size = 35, normalized size = 0.81 \[ -\frac {20 \, a^{3} x^{3} + 45 \, a^{2} b x^{2} + 36 \, a b^{2} x + 10 \, b^{3}}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 35, normalized size = 0.81 \[ -\frac {20 \, a^{3} x^{3} + 45 \, a^{2} b x^{2} + 36 \, a b^{2} x + 10 \, b^{3}}{60 \, x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 36, normalized size = 0.84 \[ -\frac {a^{3}}{3 x^{3}}-\frac {3 a^{2} b}{4 x^{4}}-\frac {3 a \,b^{2}}{5 x^{5}}-\frac {b^{3}}{6 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.98, size = 35, normalized size = 0.81 \[ -\frac {20 \, a^{3} x^{3} + 45 \, a^{2} b x^{2} + 36 \, a b^{2} x + 10 \, b^{3}}{60 \, x^{6}} \]
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 \[ -\frac {\frac {a^3\,x^3}{3}+\frac {3\,a^2\,b\,x^2}{4}+\frac {3\,a\,b^2\,x}{5}+\frac {b^3}{6}}{x^6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, size = 37, normalized size = 0.86 \[ \frac {- 20 a^{3} x^{3} - 45 a^{2} b x^{2} - 36 a b^{2} x - 10 b^{3}}{60 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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