Optimal. Leaf size=20 \[ -11+e^{e^x}+\frac {5 e^{3+e^x}}{x}+x \]
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Rubi [F]
time = 0.15, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {x^2+e^{e^x+x} x^2+e^{3+e^x} \left (-5+5 e^x x\right )}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {e^{e^x+x} \left (5 e^3+x\right )}{x}+\frac {-5 e^{3+e^x}+x^2}{x^2}\right ) \, dx\\ &=\int \frac {e^{e^x+x} \left (5 e^3+x\right )}{x} \, dx+\int \frac {-5 e^{3+e^x}+x^2}{x^2} \, dx\\ &=\int \left (1-\frac {5 e^{3+e^x}}{x^2}\right ) \, dx+\int \left (e^{e^x+x}+\frac {5 e^{3+e^x+x}}{x}\right ) \, dx\\ &=x-5 \int \frac {e^{3+e^x}}{x^2} \, dx+5 \int \frac {e^{3+e^x+x}}{x} \, dx+\int e^{e^x+x} \, dx\\ &=x-5 \int \frac {e^{3+e^x}}{x^2} \, dx+5 \int \frac {e^{3+e^x+x}}{x} \, dx+\text {Subst}\left (\int e^x \, dx,x,e^x\right )\\ &=e^{e^x}+x-5 \int \frac {e^{3+e^x}}{x^2} \, dx+5 \int \frac {e^{3+e^x+x}}{x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 19, normalized size = 0.95 \begin {gather*} e^{e^x}+\frac {5 e^{3+e^x}}{x}+x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 16, normalized size = 0.80
method | result | size |
risch | \(x +\frac {\left (5 \,{\mathrm e}^{3}+x \right ) {\mathrm e}^{{\mathrm e}^{x}}}{x}\) | \(16\) |
norman | \(\frac {x^{2}+x \,{\mathrm e}^{{\mathrm e}^{x}}+5 \,{\mathrm e}^{3} {\mathrm e}^{{\mathrm e}^{x}}}{x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 15, normalized size = 0.75 \begin {gather*} x + \frac {{\left (x + 5 \, e^{3}\right )} e^{\left (e^{x}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 27, normalized size = 1.35 \begin {gather*} \frac {{\left (x^{2} e^{x} + {\left (x + 5 \, e^{3}\right )} e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 14, normalized size = 0.70 \begin {gather*} x + \frac {\left (x + 5 e^{3}\right ) e^{e^{x}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 30, normalized size = 1.50 \begin {gather*} \frac {{\left (x^{2} e^{x} + x e^{\left (x + e^{x}\right )} + 5 \, e^{\left (x + e^{x} + 3\right )}\right )} e^{\left (-x\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.65, size = 15, normalized size = 0.75 \begin {gather*} x+{\mathrm {e}}^{{\mathrm {e}}^x}+\frac {5\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^3}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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