Optimal. Leaf size=21 \[ \frac {2}{3} a x^{3/2}+\frac {2}{11} c x^{11/2} \]
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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 = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {14} \[ \frac {2}{3} a x^{3/2}+\frac {2}{11} c x^{11/2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \sqrt {x} \left (a+c x^4\right ) \, dx &=\int \left (a \sqrt {x}+c x^{9/2}\right ) \, dx\\ &=\frac {2}{3} a x^{3/2}+\frac {2}{11} c x^{11/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.00 \[ \frac {2}{3} a x^{3/2}+\frac {2}{11} c x^{11/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 16, normalized size = 0.76 \[ \frac {2}{33} \, {\left (3 \, c x^{5} + 11 \, a x\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 13, normalized size = 0.62 \[ \frac {2}{11} \, c x^{\frac {11}{2}} + \frac {2}{3} \, a x^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.76 \[ \frac {2 \left (3 c \,x^{4}+11 a \right ) x^{\frac {3}{2}}}{33} \]
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 \[ \frac {2}{11} \, c x^{\frac {11}{2}} + \frac {2}{3} \, a x^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 15, normalized size = 0.71 \[ \frac {2\,x^{3/2}\,\left (3\,c\,x^4+11\,a\right )}{33} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.78, size = 19, normalized size = 0.90 \[ \frac {2 a x^{\frac {3}{2}}}{3} + \frac {2 c x^{\frac {11}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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