Optimal. Leaf size=47 \[ -\frac {a^3}{5 x^5}-\frac {2 a^2 b}{3 x^{9/2}}-\frac {3 a b^2}{4 x^4}-\frac {2 b^3}{7 x^{7/2}} \]
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Rubi [A] time = 0.02, antiderivative size = 47, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {266, 43} \[ -\frac {2 a^2 b}{3 x^{9/2}}-\frac {a^3}{5 x^5}-\frac {3 a b^2}{4 x^4}-\frac {2 b^3}{7 x^{7/2}} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b \sqrt {x}\right )^3}{x^6} \, dx &=2 \operatorname {Subst}\left (\int \frac {(a+b x)^3}{x^{11}} \, dx,x,\sqrt {x}\right )\\ &=2 \operatorname {Subst}\left (\int \left (\frac {a^3}{x^{11}}+\frac {3 a^2 b}{x^{10}}+\frac {3 a b^2}{x^9}+\frac {b^3}{x^8}\right ) \, dx,x,\sqrt {x}\right )\\ &=-\frac {a^3}{5 x^5}-\frac {2 a^2 b}{3 x^{9/2}}-\frac {3 a b^2}{4 x^4}-\frac {2 b^3}{7 x^{7/2}}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 41, normalized size = 0.87 \[ -\frac {84 a^3+280 a^2 b \sqrt {x}+315 a b^2 x+120 b^3 x^{3/2}}{420 x^5} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.88, size = 36, normalized size = 0.77 \[ -\frac {315 \, a b^{2} x + 84 \, a^{3} + 40 \, {\left (3 \, b^{3} x + 7 \, a^{2} b\right )} \sqrt {x}}{420 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 35, normalized size = 0.74 \[ -\frac {120 \, b^{3} x^{\frac {3}{2}} + 315 \, a b^{2} x + 280 \, a^{2} b \sqrt {x} + 84 \, a^{3}}{420 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 36, normalized size = 0.77 \[ -\frac {2 b^{3}}{7 x^{\frac {7}{2}}}-\frac {3 a \,b^{2}}{4 x^{4}}-\frac {2 a^{2} b}{3 x^{\frac {9}{2}}}-\frac {a^{3}}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.90, size = 35, normalized size = 0.74 \[ -\frac {120 \, b^{3} x^{\frac {3}{2}} + 315 \, a b^{2} x + 280 \, a^{2} b \sqrt {x} + 84 \, a^{3}}{420 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 35, normalized size = 0.74 \[ -\frac {84\,a^3+120\,b^3\,x^{3/2}+280\,a^2\,b\,\sqrt {x}+315\,a\,b^2\,x}{420\,x^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.22, size = 46, normalized size = 0.98 \[ - \frac {a^{3}}{5 x^{5}} - \frac {2 a^{2} b}{3 x^{\frac {9}{2}}} - \frac {3 a b^{2}}{4 x^{4}} - \frac {2 b^{3}}{7 x^{\frac {7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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