Optimal. Leaf size=16 \[ 2+e^x+\frac {5}{2 x^2}+x+x^2 \]
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Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 0.94, number of steps used = 5, number of rules used = 2, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {14, 2194} \begin {gather*} x^2+\frac {5}{2 x^2}+x+e^x \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^x+\frac {-5+x^3+2 x^4}{x^3}\right ) \, dx\\ &=\int e^x \, dx+\int \frac {-5+x^3+2 x^4}{x^3} \, dx\\ &=e^x+\int \left (1-\frac {5}{x^3}+2 x\right ) \, dx\\ &=e^x+\frac {5}{2 x^2}+x+x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 0.94 \begin {gather*} e^x+\frac {5}{2 x^2}+x+x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 24, normalized size = 1.50 \begin {gather*} \frac {2 \, x^{4} + 2 \, x^{3} + 2 \, x^{2} e^{x} + 5}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.20, size = 24, normalized size = 1.50 \begin {gather*} \frac {2 \, x^{4} + 2 \, x^{3} + 2 \, x^{2} e^{x} + 5}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 13, normalized size = 0.81
method | result | size |
default | \(x^{2}+x +\frac {5}{2 x^{2}}+{\mathrm e}^{x}\) | \(13\) |
risch | \(x^{2}+x +\frac {5}{2 x^{2}}+{\mathrm e}^{x}\) | \(13\) |
norman | \(\frac {\frac {5}{2}+{\mathrm e}^{x} x^{2}+x^{4}+x^{3}}{x^{2}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 12, normalized size = 0.75 \begin {gather*} x^{2} + x + \frac {5}{2 \, x^{2}} + e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.20, size = 12, normalized size = 0.75 \begin {gather*} x+{\mathrm {e}}^x+\frac {5}{2\,x^2}+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 14, normalized size = 0.88 \begin {gather*} x^{2} + x + e^{x} + \frac {5}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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