Optimal. Leaf size=21 \[ \frac {2}{7} a x^{7/2}+\frac {2}{15} c x^{15/2} \]
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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}
\begin {gather*} \frac {2}{7} a x^{7/2}+\frac {2}{15} c x^{15/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int x^{5/2} \left (a+c x^4\right ) \, dx &=\int \left (a x^{5/2}+c x^{13/2}\right ) \, dx\\ &=\frac {2}{7} a x^{7/2}+\frac {2}{15} c x^{15/2}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 21, normalized size = 1.00 \begin {gather*} \frac {2}{105} \left (15 a x^{7/2}+7 c x^{15/2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 14, normalized size = 0.67
method | result | size |
derivativedivides | \(\frac {2 a \,x^{\frac {7}{2}}}{7}+\frac {2 c \,x^{\frac {15}{2}}}{15}\) | \(14\) |
default | \(\frac {2 a \,x^{\frac {7}{2}}}{7}+\frac {2 c \,x^{\frac {15}{2}}}{15}\) | \(14\) |
gosper | \(\frac {2 x^{\frac {7}{2}} \left (7 x^{4} c +15 a \right )}{105}\) | \(16\) |
trager | \(\frac {2 x^{\frac {7}{2}} \left (7 x^{4} c +15 a \right )}{105}\) | \(16\) |
risch | \(\frac {2 x^{\frac {7}{2}} \left (7 x^{4} c +15 a \right )}{105}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 13, normalized size = 0.62 \begin {gather*} \frac {2}{15} \, c x^{\frac {15}{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 = 0.37, size = 18, normalized size = 0.86 \begin {gather*} \frac {2}{105} \, {\left (7 \, c x^{7} + 15 \, 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 = 0.47, size = 19, normalized size = 0.90 \begin {gather*} \frac {2 a x^{\frac {7}{2}}}{7} + \frac {2 c x^{\frac {15}{2}}}{15} \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}{15} \, c x^{\frac {15}{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 = 1.05, size = 15, normalized size = 0.71 \begin {gather*} \frac {2\,x^{7/2}\,\left (7\,c\,x^4+15\,a\right )}{105} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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