Optimal. Leaf size=19 \[ -\frac{a}{3 x^3}-\frac{2 b}{5 x^{5/2}} \]
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Rubi [A] time = 0.004937, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {14} \[ -\frac{a}{3 x^3}-\frac{2 b}{5 x^{5/2}} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{a+b \sqrt{x}}{x^4} \, dx &=\int \left (\frac{a}{x^4}+\frac{b}{x^{7/2}}\right ) \, dx\\ &=-\frac{a}{3 x^3}-\frac{2 b}{5 x^{5/2}}\\ \end{align*}
Mathematica [A] time = 0.0068429, size = 19, normalized size = 1. \[ -\frac{a}{3 x^3}-\frac{2 b}{5 x^{5/2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 14, normalized size = 0.7 \begin{align*} -{\frac{a}{3\,{x}^{3}}}-{\frac{2\,b}{5}{x}^{-{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.961646, size = 20, normalized size = 1.05 \begin{align*} -\frac{6 \, b \sqrt{x} + 5 \, a}{15 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.51372, size = 42, normalized size = 2.21 \begin{align*} -\frac{6 \, b \sqrt{x} + 5 \, a}{15 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.884565, size = 17, normalized size = 0.89 \begin{align*} - \frac{a}{3 x^{3}} - \frac{2 b}{5 x^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08902, size = 20, normalized size = 1.05 \begin{align*} -\frac{6 \, b \sqrt{x} + 5 \, a}{15 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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