Optimal. Leaf size=21 \[ \frac {2}{7} a x^{7/2}+\frac {2}{9} b x^{9/2} \]
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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 = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {43} \[ \frac {2}{7} a x^{7/2}+\frac {2}{9} b x^{9/2} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int x^{5/2} (a+b x) \, dx &=\int \left (a x^{5/2}+b x^{7/2}\right ) \, dx\\ &=\frac {2}{7} a x^{7/2}+\frac {2}{9} b x^{9/2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 0.81 \[ \frac {2}{63} x^{7/2} (9 a+7 b x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 18, normalized size = 0.86 \[ \frac {2}{63} \, {\left (7 \, b x^{4} + 9 \, a x^{3}\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.83, size = 13, normalized size = 0.62 \[ \frac {2}{9} \, b x^{\frac {9}{2}} + \frac {2}{7} \, a x^{\frac {7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.67 \[ \frac {2 \left (7 b x +9 a \right ) x^{\frac {7}{2}}}{63} \]
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 \[ \frac {2}{9} \, b x^{\frac {9}{2}} + \frac {2}{7} \, a x^{\frac {7}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 13, normalized size = 0.62 \[ \frac {2\,x^{7/2}\,\left (9\,a+7\,b\,x\right )}{63} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.59, size = 19, normalized size = 0.90 \[ \frac {2 a x^{\frac {7}{2}}}{7} + \frac {2 b x^{\frac {9}{2}}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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