Optimal. Leaf size=21 \[ -\frac {\left (a+b \sqrt {x}\right )^4}{2 a x^2} \]
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Rubi [A] time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {264} \[ -\frac {\left (a+b \sqrt {x}\right )^4}{2 a x^2} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int \frac {\left (a+b \sqrt {x}\right )^3}{x^3} \, dx &=-\frac {\left (a+b \sqrt {x}\right )^4}{2 a x^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 1.00 \[ -\frac {\left (a+b \sqrt {x}\right )^4}{2 a x^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.08, size = 32, normalized size = 1.52 \[ -\frac {6 \, a b^{2} x + a^{3} + 4 \, {\left (b^{3} x + a^{2} b\right )} \sqrt {x}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 33, normalized size = 1.57 \[ -\frac {4 \, b^{3} x^{\frac {3}{2}} + 6 \, a b^{2} x + 4 \, a^{2} b \sqrt {x} + a^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 36, normalized size = 1.71 \[ -\frac {2 b^{3}}{\sqrt {x}}-\frac {3 a \,b^{2}}{x}-\frac {2 a^{2} b}{x^{\frac {3}{2}}}-\frac {a^{3}}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.81, size = 33, normalized size = 1.57 \[ -\frac {4 \, b^{3} x^{\frac {3}{2}} + 6 \, a b^{2} x + 4 \, a^{2} b \sqrt {x} + a^{3}}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 33, normalized size = 1.57 \[ -\frac {a^3+4\,b^3\,x^{3/2}+4\,a^2\,b\,\sqrt {x}+6\,a\,b^2\,x}{2\,x^2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.69, size = 39, normalized size = 1.86 \[ - \frac {a^{3}}{2 x^{2}} - \frac {2 a^{2} b}{x^{\frac {3}{2}}} - \frac {3 a b^{2}}{x} - \frac {2 b^{3}}{\sqrt {x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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