Optimal. Leaf size=21 \[ \frac {2}{9} b x^{9/2}+\frac {2}{13} c x^{13/2} \]
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Rubi [A] time = 0.00, 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} \[ \frac {2}{9} b x^{9/2}+\frac {2}{13} c x^{13/2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int x^{3/2} \left (b x^2+c x^4\right ) \, dx &=\int \left (b x^{7/2}+c x^{11/2}\right ) \, dx\\ &=\frac {2}{9} b x^{9/2}+\frac {2}{13} c x^{13/2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 1.00 \[ \frac {2}{9} b x^{9/2}+\frac {2}{13} c x^{13/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.74, size = 18, normalized size = 0.86 \[ \frac {2}{117} \, {\left (9 \, c x^{6} + 13 \, b x^{4}\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 13, normalized size = 0.62 \[ \frac {2}{13} \, c x^{\frac {13}{2}} + \frac {2}{9} \, b x^{\frac {9}{2}} \]
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 \[ \frac {2 \left (9 c \,x^{2}+13 b \right ) x^{\frac {9}{2}}}{117} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 13, normalized size = 0.62 \[ \frac {2}{13} \, c x^{\frac {13}{2}} + \frac {2}{9} \, b x^{\frac {9}{2}} \]
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 \[ \frac {2\,x^{9/2}\,\left (9\,c\,x^2+13\,b\right )}{117} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.53, size = 19, normalized size = 0.90 \[ \frac {2 b x^{\frac {9}{2}}}{9} + \frac {2 c x^{\frac {13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
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