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 = 0.01, antiderivative size = 21, 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} \begin {gather*} \frac {2}{5} b x^{5/2}+\frac {2}{9} c x^{9/2} \end {gather*}
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*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 1.00 \begin {gather*} \frac {2}{5} b x^{5/2}+\frac {2}{9} c x^{9/2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.02, size = 21, normalized size = 1.00 \begin {gather*} \frac {2}{45} \left (9 b x^{5/2}+5 c x^{9/2}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.97, size = 18, normalized size = 0.86 \begin {gather*} \frac {2}{45} \, {\left (5 \, c x^{4} + 9 \, b x^{2}\right )} \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 13, normalized size = 0.62 \begin {gather*} \frac {2}{9} \, c x^{\frac {9}{2}} + \frac {2}{5} \, b x^{\frac {5}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.76 \begin {gather*} \frac {2 \left (5 c \,x^{2}+9 b \right ) x^{\frac {5}{2}}}{45} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 13, normalized size = 0.62 \begin {gather*} \frac {2}{9} \, c x^{\frac {9}{2}} + \frac {2}{5} \, b x^{\frac {5}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 15, normalized size = 0.71 \begin {gather*} \frac {2\,x^{5/2}\,\left (5\,c\,x^2+9\,b\right )}{45} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.78, size = 19, normalized size = 0.90 \begin {gather*} \frac {2 b x^{\frac {5}{2}}}{5} + \frac {2 c x^{\frac {9}{2}}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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