Optimal. Leaf size=19 \[ 5 \left (x+49 e^x \left (4+e^{5/x}+x\right )\right ) \]
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Rubi [A]
time = 0.25, antiderivative size = 26, normalized size of antiderivative = 1.37, number of steps
used = 9, number of rules used = 6, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {14, 6820, 6874,
2225, 2207, 6838} \begin {gather*} 245 e^x x+5 x+980 e^x+245 e^{x+\frac {5}{x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2207
Rule 2225
Rule 6820
Rule 6838
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (5+\frac {245 e^x \left (-5 e^{5/x}+5 x^2+e^{5/x} x^2+x^3\right )}{x^2}\right ) \, dx\\ &=5 x+245 \int \frac {e^x \left (-5 e^{5/x}+5 x^2+e^{5/x} x^2+x^3\right )}{x^2} \, dx\\ &=5 x+245 \int e^x \left (5+e^{5/x} \left (1-\frac {5}{x^2}\right )+x\right ) \, dx\\ &=5 x+245 \int \left (5 e^x+e^x x+\frac {e^{\frac {5}{x}+x} \left (-5+x^2\right )}{x^2}\right ) \, dx\\ &=5 x+245 \int e^x x \, dx+245 \int \frac {e^{\frac {5}{x}+x} \left (-5+x^2\right )}{x^2} \, dx+1225 \int e^x \, dx\\ &=1225 e^x+245 e^{\frac {5}{x}+x}+5 x+245 e^x x-245 \int e^x \, dx\\ &=980 e^x+245 e^{\frac {5}{x}+x}+5 x+245 e^x x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 23, normalized size = 1.21 \begin {gather*} 245 e^{\frac {5}{x}+x}+5 x+245 e^x (4+x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.86, size = 25, normalized size = 1.32
method | result | size |
risch | \(5 x +\left (980+245 x \right ) {\mathrm e}^{x}+245 \,{\mathrm e}^{\frac {x^{2}+5}{x}}\) | \(25\) |
norman | \(\frac {5 x^{2}+980 \,{\mathrm e}^{x} x +245 \,{\mathrm e}^{x} x^{2}+245 \,{\mathrm e}^{\frac {5}{x}} x \,{\mathrm e}^{x}}{x}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 25, normalized size = 1.32 \begin {gather*} 245 \, {\left (x - 1\right )} e^{x} + 5 \, x + 245 \, e^{\left (x + \frac {5}{x}\right )} + 1225 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 17, normalized size = 0.89 \begin {gather*} 245 \, {\left (x + e^{\frac {5}{x}} + 4\right )} e^{x} + 5 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.36, size = 17, normalized size = 0.89 \begin {gather*} 5 x + \left (245 x + 245 e^{\frac {5}{x}} + 980\right ) e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 25, normalized size = 1.32 \begin {gather*} 245 \, x e^{x} + 5 \, x + 980 \, e^{x} + 245 \, e^{\left (\frac {x^{2} + 5}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.29, size = 23, normalized size = 1.21 \begin {gather*} 5\,x+245\,{\mathrm {e}}^{x+\frac {5}{x}}+980\,{\mathrm {e}}^x+245\,x\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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