Optimal. Leaf size=16 \[ \frac {x^2}{2}+5 x+\frac {4}{x} \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {14} \[ \frac {x^2}{2}+5 x+\frac {4}{x} \]
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {-4+5 x^2+x^3}{x^2} \, dx &=\int \left (5-\frac {4}{x^2}+x\right ) \, dx\\ &=\frac {4}{x}+5 x+\frac {x^2}{2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ \frac {x^2}{2}+5 x+\frac {4}{x} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 15, normalized size = 0.94 \[ \frac {x^{3} + 10 \, x^{2} + 8}{2 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.31, size = 14, normalized size = 0.88 \[ \frac {1}{2} \, x^{2} + 5 \, x + \frac {4}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.94 \[ \frac {x^{2}}{2}+5 x +\frac {4}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 14, normalized size = 0.88 \[ \frac {1}{2} \, x^{2} + 5 \, x + \frac {4}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 15, normalized size = 0.94 \[ \frac {x^3+10\,x^2+8}{2\,x} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 10, normalized size = 0.62 \[ \frac {x^{2}}{2} + 5 x + \frac {4}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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