Optimal. Leaf size=21 \[ -\frac {2 a}{5 x^{5/2}}+\frac {2}{3} c x^{3/2} \]
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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}{3} c x^{3/2}-\frac {2 a}{5 x^{5/2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+c x^4}{x^{7/2}} \, dx &=\int \left (\frac {a}{x^{7/2}}+c \sqrt {x}\right ) \, dx\\ &=-\frac {2 a}{5 x^{5/2}}+\frac {2}{3} c x^{3/2}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 19, normalized size = 0.90 \begin {gather*} -\frac {2 \left (3 a-5 c x^4\right )}{15 x^{5/2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 14, normalized size = 0.67
method | result | size |
derivativedivides | \(-\frac {2 a}{5 x^{\frac {5}{2}}}+\frac {2 c \,x^{\frac {3}{2}}}{3}\) | \(14\) |
default | \(-\frac {2 a}{5 x^{\frac {5}{2}}}+\frac {2 c \,x^{\frac {3}{2}}}{3}\) | \(14\) |
gosper | \(-\frac {2 \left (-5 x^{4} c +3 a \right )}{15 x^{\frac {5}{2}}}\) | \(16\) |
trager | \(-\frac {2 \left (-5 x^{4} c +3 a \right )}{15 x^{\frac {5}{2}}}\) | \(16\) |
risch | \(-\frac {2 \left (-5 x^{4} c +3 a \right )}{15 x^{\frac {5}{2}}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 13, normalized size = 0.62 \begin {gather*} \frac {2}{3} \, c x^{\frac {3}{2}} - \frac {2 \, a}{5 \, x^{\frac {5}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 15, normalized size = 0.71 \begin {gather*} \frac {2 \, {\left (5 \, c x^{4} - 3 \, a\right )}}{15 \, x^{\frac {5}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.34, size = 19, normalized size = 0.90 \begin {gather*} - \frac {2 a}{5 x^{\frac {5}{2}}} + \frac {2 c x^{\frac {3}{2}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.91, size = 13, normalized size = 0.62 \begin {gather*} \frac {2}{3} \, c x^{\frac {3}{2}} - \frac {2 \, a}{5 \, x^{\frac {5}{2}}} \end {gather*}
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 \begin {gather*} -\frac {6\,a-10\,c\,x^4}{15\,x^{5/2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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