Optimal. Leaf size=21 \[ \frac{2}{3} b x^{3/2}+\frac{2}{7} c x^{7/2} \]
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Rubi [A] time = 0.0051502, 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} \[ \frac{2}{3} b x^{3/2}+\frac{2}{7} c x^{7/2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin{align*} \int \frac{b x^2+c x^4}{x^{3/2}} \, dx &=\int \left (b \sqrt{x}+c x^{5/2}\right ) \, dx\\ &=\frac{2}{3} b x^{3/2}+\frac{2}{7} c x^{7/2}\\ \end{align*}
Mathematica [A] time = 0.0044157, size = 21, normalized size = 1. \[ \frac{2}{3} b x^{3/2}+\frac{2}{7} c x^{7/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 16, normalized size = 0.8 \begin{align*}{\frac{6\,c{x}^{2}+14\,b}{21}{x}^{{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.953166, size = 18, normalized size = 0.86 \begin{align*} \frac{2}{7} \, c x^{\frac{7}{2}} + \frac{2}{3} \, b x^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.29651, size = 43, normalized size = 2.05 \begin{align*} \frac{2}{21} \,{\left (3 \, c x^{3} + 7 \, b x\right )} \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.915969, size = 19, normalized size = 0.9 \begin{align*} \frac{2 b x^{\frac{3}{2}}}{3} + \frac{2 c x^{\frac{7}{2}}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12433, size = 18, normalized size = 0.86 \begin{align*} \frac{2}{7} \, c x^{\frac{7}{2}} + \frac{2}{3} \, b x^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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