Optimal. Leaf size=27 \[ -5+\frac {16}{x}+2 \left (4+e^3-x+\left (1+e^5+x^2\right )^2\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 24, normalized size of antiderivative = 0.89, number of steps used = 3, number of rules used = 2, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {6, 14} \begin {gather*} 2 x^4+4 \left (1+e^5\right ) x^2-2 x+\frac {16}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-16-2 x^2+\left (8+8 e^5\right ) x^3+8 x^5}{x^2} \, dx\\ &=\int \left (-2-\frac {16}{x^2}+8 \left (1+e^5\right ) x+8 x^3\right ) \, dx\\ &=\frac {16}{x}-2 x+4 \left (1+e^5\right ) x^2+2 x^4\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 24, normalized size = 0.89 \begin {gather*} \frac {16}{x}-2 x+4 \left (1+e^5\right ) x^2+2 x^4 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.72, size = 27, normalized size = 1.00 \begin {gather*} \frac {2 \, {\left (x^{5} + 2 \, x^{3} e^{5} + 2 \, x^{3} - x^{2} + 8\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 26, normalized size = 0.96 \begin {gather*} 2 \, x^{4} + 4 \, x^{2} e^{5} + 4 \, x^{2} - 2 \, x + \frac {16}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 27, normalized size = 1.00
method | result | size |
default | \(2 x^{4}+4 x^{2} {\mathrm e}^{5}+4 x^{2}-2 x +\frac {16}{x}\) | \(27\) |
norman | \(\frac {16+\left (4 \,{\mathrm e}^{5}+4\right ) x^{3}-2 x^{2}+2 x^{5}}{x}\) | \(27\) |
risch | \(2 x^{4}+4 x^{2} {\mathrm e}^{5}+4 x^{2}-2 x +\frac {16}{x}\) | \(27\) |
gosper | \(\frac {2 x^{5}+4 x^{3} {\mathrm e}^{5}+4 x^{3}-2 x^{2}+16}{x}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 23, normalized size = 0.85 \begin {gather*} 2 \, x^{4} + 4 \, x^{2} {\left (e^{5} + 1\right )} - 2 \, x + \frac {16}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 24, normalized size = 0.89 \begin {gather*} x^2\,\left (4\,{\mathrm {e}}^5+4\right )-2\,x+\frac {16}{x}+2\,x^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 20, normalized size = 0.74 \begin {gather*} 2 x^{4} + x^{2} \left (4 + 4 e^{5}\right ) - 2 x + \frac {16}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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