Optimal. Leaf size=29 \[ -\frac {2 a}{5 x^{5/2}}-\frac {2 b}{\sqrt {x}}+\frac {2}{3} c x^{3/2} \]
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Rubi [A] time = 0.01, antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {14} \[ -\frac {2 a}{5 x^{5/2}}-\frac {2 b}{\sqrt {x}}+\frac {2}{3} c x^{3/2} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a+b x^2+c x^4}{x^{7/2}} \, dx &=\int \left (\frac {a}{x^{7/2}}+\frac {b}{x^{3/2}}+c \sqrt {x}\right ) \, dx\\ &=-\frac {2 a}{5 x^{5/2}}-\frac {2 b}{\sqrt {x}}+\frac {2}{3} c x^{3/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 25, normalized size = 0.86 \[ \frac {2 \left (-3 a-15 b x^2+5 c x^4\right )}{15 x^{5/2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 21, normalized size = 0.72 \[ \frac {2 \, {\left (5 \, c x^{4} - 15 \, b x^{2} - 3 \, a\right )}}{15 \, x^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 20, normalized size = 0.69 \[ \frac {2}{3} \, c x^{\frac {3}{2}} - \frac {2 \, {\left (5 \, b x^{2} + a\right )}}{5 \, x^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 22, normalized size = 0.76 \[ -\frac {2 \left (-5 c \,x^{4}+15 b \,x^{2}+3 a \right )}{15 x^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.08, size = 20, normalized size = 0.69 \[ \frac {2}{3} \, c x^{\frac {3}{2}} - \frac {2 \, {\left (5 \, b x^{2} + a\right )}}{5 \, x^{\frac {5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.33, size = 21, normalized size = 0.72 \[ -\frac {-10\,c\,x^4+30\,b\,x^2+6\,a}{15\,x^{5/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.87, size = 27, normalized size = 0.93 \[ - \frac {2 a}{5 x^{\frac {5}{2}}} - \frac {2 b}{\sqrt {x}} + \frac {2 c x^{\frac {3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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