Optimal. Leaf size=36 \[ \frac {2}{9} b^2 x^{9/2}+\frac {4}{13} b c x^{13/2}+\frac {2}{17} c^2 x^{17/2} \]
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Rubi [A] time = 0.01, antiderivative size = 36, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {1584, 270} \[ \frac {2}{9} b^2 x^{9/2}+\frac {4}{13} b c x^{13/2}+\frac {2}{17} c^2 x^{17/2} \]
Antiderivative was successfully verified.
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Rule 270
Rule 1584
Rubi steps
\begin {align*} \int \frac {\left (b x^2+c x^4\right )^2}{\sqrt {x}} \, dx &=\int x^{7/2} \left (b+c x^2\right )^2 \, dx\\ &=\int \left (b^2 x^{7/2}+2 b c x^{11/2}+c^2 x^{15/2}\right ) \, dx\\ &=\frac {2}{9} b^2 x^{9/2}+\frac {4}{13} b c x^{13/2}+\frac {2}{17} c^2 x^{17/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 30, normalized size = 0.83 \[ \frac {2 x^{9/2} \left (221 b^2+306 b c x^2+117 c^2 x^4\right )}{1989} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 29, normalized size = 0.81 \[ \frac {2}{1989} \, {\left (117 \, c^{2} x^{8} + 306 \, b c x^{6} + 221 \, b^{2} x^{4}\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 24, normalized size = 0.67 \[ \frac {2}{17} \, c^{2} x^{\frac {17}{2}} + \frac {4}{13} \, b c x^{\frac {13}{2}} + \frac {2}{9} \, b^{2} x^{\frac {9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 27, normalized size = 0.75 \[ \frac {2 \left (117 c^{2} x^{4}+306 b c \,x^{2}+221 b^{2}\right ) x^{\frac {9}{2}}}{1989} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.25, size = 24, normalized size = 0.67 \[ \frac {2}{17} \, c^{2} x^{\frac {17}{2}} + \frac {4}{13} \, b c x^{\frac {13}{2}} + \frac {2}{9} \, b^{2} x^{\frac {9}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 25, normalized size = 0.69 \[ x^{9/2}\,\left (\frac {2\,b^2}{9}+\frac {4\,b\,c\,x^2}{13}+\frac {2\,c^2\,x^4}{17}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 4.98, size = 34, normalized size = 0.94 \[ \frac {2 b^{2} x^{\frac {9}{2}}}{9} + \frac {4 b c x^{\frac {13}{2}}}{13} + \frac {2 c^{2} x^{\frac {17}{2}}}{17} \]
Verification of antiderivative is not currently implemented for this CAS.
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