Optimal. Leaf size=32 \[ -\frac{a^2}{4 x^4}-\frac{4 a b}{7 x^{7/2}}-\frac{b^2}{3 x^3} \]
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Rubi [A] time = 0.0142292, antiderivative size = 32, normalized size of antiderivative = 1., 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} \[ -\frac{a^2}{4 x^4}-\frac{4 a b}{7 x^{7/2}}-\frac{b^2}{3 x^3} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{\left (a+b \sqrt{x}\right )^2}{x^5} \, dx &=2 \operatorname{Subst}\left (\int \frac{(a+b x)^2}{x^9} \, dx,x,\sqrt{x}\right )\\ &=2 \operatorname{Subst}\left (\int \left (\frac{a^2}{x^9}+\frac{2 a b}{x^8}+\frac{b^2}{x^7}\right ) \, dx,x,\sqrt{x}\right )\\ &=-\frac{a^2}{4 x^4}-\frac{4 a b}{7 x^{7/2}}-\frac{b^2}{3 x^3}\\ \end{align*}
Mathematica [A] time = 0.0109708, size = 28, normalized size = 0.88 \[ -\frac{21 a^2+48 a b \sqrt{x}+28 b^2 x}{84 x^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 25, normalized size = 0.8 \begin{align*} -{\frac{{a}^{2}}{4\,{x}^{4}}}-{\frac{4\,ab}{7}{x}^{-{\frac{7}{2}}}}-{\frac{{b}^{2}}{3\,{x}^{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.977787, size = 32, normalized size = 1. \begin{align*} -\frac{28 \, b^{2} x + 48 \, a b \sqrt{x} + 21 \, a^{2}}{84 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.47106, size = 65, normalized size = 2.03 \begin{align*} -\frac{28 \, b^{2} x + 48 \, a b \sqrt{x} + 21 \, a^{2}}{84 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.34353, size = 29, normalized size = 0.91 \begin{align*} - \frac{a^{2}}{4 x^{4}} - \frac{4 a b}{7 x^{\frac{7}{2}}} - \frac{b^{2}}{3 x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09991, size = 32, normalized size = 1. \begin{align*} -\frac{28 \, b^{2} x + 48 \, a b \sqrt{x} + 21 \, a^{2}}{84 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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