Optimal. Leaf size=21 \[ \frac{2}{5} b x^{5/2}+\frac{2}{9} c x^{9/2} \]
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Rubi [A] time = 0.0050601, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {14} \[ \frac{2}{5} b x^{5/2}+\frac{2}{9} c x^{9/2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{b x^2+c x^4}{\sqrt{x}} \, dx &=\int \left (b x^{3/2}+c x^{7/2}\right ) \, dx\\ &=\frac{2}{5} b x^{5/2}+\frac{2}{9} c x^{9/2}\\ \end{align*}
Mathematica [A] time = 0.0054225, size = 21, normalized size = 1. \[ \frac{2}{5} b x^{5/2}+\frac{2}{9} c x^{9/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 16, normalized size = 0.8 \begin{align*}{\frac{10\,c{x}^{2}+18\,b}{45}{x}^{{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.958717, size = 18, normalized size = 0.86 \begin{align*} \frac{2}{9} \, c x^{\frac{9}{2}} + \frac{2}{5} \, b x^{\frac{5}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.28677, size = 46, normalized size = 2.19 \begin{align*} \frac{2}{45} \,{\left (5 \, c x^{4} + 9 \, b x^{2}\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.762273, size = 19, normalized size = 0.9 \begin{align*} \frac{2 b x^{\frac{5}{2}}}{5} + \frac{2 c x^{\frac{9}{2}}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10424, size = 18, normalized size = 0.86 \begin{align*} \frac{2}{9} \, c x^{\frac{9}{2}} + \frac{2}{5} \, b x^{\frac{5}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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