Optimal. Leaf size=31 \[ \frac {2}{3} a x^{3/2}+\frac {2}{7} b x^{7/2}+\frac {2}{11} c x^{11/2} \]
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Rubi [A] time = 0.01, antiderivative size = 31, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {14} \[ \frac {2}{3} a x^{3/2}+\frac {2}{7} b x^{7/2}+\frac {2}{11} c x^{11/2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \sqrt {x} \left (a+b x^2+c x^4\right ) \, dx &=\int \left (a \sqrt {x}+b x^{5/2}+c x^{9/2}\right ) \, dx\\ &=\frac {2}{3} a x^{3/2}+\frac {2}{7} b x^{7/2}+\frac {2}{11} c x^{11/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 25, normalized size = 0.81 \[ \frac {2}{231} x^{3/2} \left (77 a+33 b x^2+21 c x^4\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 22, normalized size = 0.71 \[ \frac {2}{231} \, {\left (21 \, c x^{5} + 33 \, b x^{3} + 77 \, a x\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 19, normalized size = 0.61 \[ \frac {2}{11} \, c x^{\frac {11}{2}} + \frac {2}{7} \, b x^{\frac {7}{2}} + \frac {2}{3} \, a x^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 22, normalized size = 0.71 \[ \frac {2 \left (21 c \,x^{4}+33 b \,x^{2}+77 a \right ) x^{\frac {3}{2}}}{231} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.01, size = 19, normalized size = 0.61 \[ \frac {2}{11} \, c x^{\frac {11}{2}} + \frac {2}{7} \, b x^{\frac {7}{2}} + \frac {2}{3} \, a x^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 21, normalized size = 0.68 \[ \frac {2\,x^{3/2}\,\left (21\,c\,x^4+33\,b\,x^2+77\,a\right )}{231} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.10, size = 29, normalized size = 0.94 \[ \frac {2 a x^{\frac {3}{2}}}{3} + \frac {2 b x^{\frac {7}{2}}}{7} + \frac {2 c x^{\frac {11}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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