Optimal. Leaf size=17 \[ 2 b \sqrt{x}-\frac{2 a}{\sqrt{x}} \]
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Rubi [A] time = 0.0040094, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {43} \[ 2 b \sqrt{x}-\frac{2 a}{\sqrt{x}} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{a+b x}{x^{3/2}} \, dx &=\int \left (\frac{a}{x^{3/2}}+\frac{b}{\sqrt{x}}\right ) \, dx\\ &=-\frac{2 a}{\sqrt{x}}+2 b \sqrt{x}\\ \end{align*}
Mathematica [A] time = 0.0051799, size = 14, normalized size = 0.82 \[ \frac{2 (b x-a)}{\sqrt{x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 12, normalized size = 0.7 \begin{align*} -2\,{\frac{-bx+a}{\sqrt{x}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02495, size = 18, normalized size = 1.06 \begin{align*} 2 \, b \sqrt{x} - \frac{2 \, a}{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.52989, size = 28, normalized size = 1.65 \begin{align*} \frac{2 \,{\left (b x - a\right )}}{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.510208, size = 15, normalized size = 0.88 \begin{align*} - \frac{2 a}{\sqrt{x}} + 2 b \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.25551, size = 18, normalized size = 1.06 \begin{align*} 2 \, b \sqrt{x} - \frac{2 \, a}{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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