Optimal. Leaf size=21 \[ -\frac{\left (a+b \sqrt{x}\right )^4}{2 a x^2} \]
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Rubi [A] time = 0.0033667, antiderivative size = 21, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0032108, size = 21, normalized size = 1. \[ -\frac{\left (a+b \sqrt{x}\right )^4}{2 a x^2} \]
Antiderivative was successfully verified.
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Maple [B] time = 0.002, size = 36, normalized size = 1.7 \begin{align*} -2\,{\frac{{b}^{3}}{\sqrt{x}}}-3\,{\frac{{b}^{2}a}{x}}-2\,{\frac{b{a}^{2}}{{x}^{3/2}}}-{\frac{{a}^{3}}{2\,{x}^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.963568, size = 45, normalized size = 2.14 \begin{align*} -\frac{4 \, b^{3} x^{\frac{3}{2}} + 6 \, a b^{2} x + 4 \, a^{2} b \sqrt{x} + a^{3}}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.48042, size = 76, normalized size = 3.62 \begin{align*} -\frac{6 \, a b^{2} x + a^{3} + 4 \,{\left (b^{3} x + a^{2} b\right )} \sqrt{x}}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.928327, size = 39, normalized size = 1.86 \begin{align*} - \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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11296, size = 45, normalized size = 2.14 \begin{align*} -\frac{4 \, b^{3} x^{\frac{3}{2}} + 6 \, a b^{2} x + 4 \, a^{2} b \sqrt{x} + a^{3}}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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