Optimal. Leaf size=19 \[ 2 b \sqrt {x}+\frac {2}{5} c x^{5/2} \]
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Rubi [A] time = 0.00, antiderivative size = 19, normalized size of antiderivative = 1.00, 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} \[ 2 b \sqrt {x}+\frac {2}{5} c x^{5/2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {b x^2+c x^4}{x^{5/2}} \, dx &=\int \left (\frac {b}{\sqrt {x}}+c x^{3/2}\right ) \, dx\\ &=2 b \sqrt {x}+\frac {2}{5} c x^{5/2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 19, normalized size = 1.00 \[ 2 b \sqrt {x}+\frac {2}{5} c x^{5/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 14, normalized size = 0.74 \[ \frac {2}{5} \, {\left (c x^{2} + 5 \, b\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 13, normalized size = 0.68 \[ \frac {2}{5} \, c x^{\frac {5}{2}} + 2 \, b \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.79 \[ \frac {2 \left (c \,x^{2}+5 b \right ) \sqrt {x}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 13, normalized size = 0.68 \[ \frac {2}{5} \, c x^{\frac {5}{2}} + 2 \, b \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 14, normalized size = 0.74 \[ \frac {2\,\sqrt {x}\,\left (c\,x^2+5\,b\right )}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.00, size = 17, normalized size = 0.89 \[ 2 b \sqrt {x} + \frac {2 c x^{\frac {5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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