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 = {45}
\begin {gather*} \frac {2}{7} a x^{7/2}+\frac {2}{9} b x^{9/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
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 = 0.01, size = 17, normalized size = 0.81 \begin {gather*} \frac {2}{63} x^{7/2} (9 a+7 b x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 14, normalized size = 0.67
method | result | size |
gosper | \(\frac {2 x^{\frac {7}{2}} \left (7 b x +9 a \right )}{63}\) | \(14\) |
derivativedivides | \(\frac {2 a \,x^{\frac {7}{2}}}{7}+\frac {2 b \,x^{\frac {9}{2}}}{9}\) | \(14\) |
default | \(\frac {2 a \,x^{\frac {7}{2}}}{7}+\frac {2 b \,x^{\frac {9}{2}}}{9}\) | \(14\) |
trager | \(\frac {2 x^{\frac {7}{2}} \left (7 b x +9 a \right )}{63}\) | \(14\) |
risch | \(\frac {2 x^{\frac {7}{2}} \left (7 b x +9 a \right )}{63}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 13, normalized size = 0.62 \begin {gather*} \frac {2}{9} \, b x^{\frac {9}{2}} + \frac {2}{7} \, a x^{\frac {7}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.46, size = 18, normalized size = 0.86 \begin {gather*} \frac {2}{63} \, {\left (7 \, b x^{4} + 9 \, a x^{3}\right )} \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.20, size = 19, normalized size = 0.90 \begin {gather*} \frac {2 a x^{\frac {7}{2}}}{7} + \frac {2 b x^{\frac {9}{2}}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.12, size = 13, normalized size = 0.62 \begin {gather*} \frac {2}{9} \, b x^{\frac {9}{2}} + \frac {2}{7} \, a x^{\frac {7}{2}} \end {gather*}
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 \begin {gather*} \frac {2\,x^{7/2}\,\left (9\,a+7\,b\,x\right )}{63} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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