Integrand size = 40, antiderivative size = 19 \[ \int \frac {5 x^2+e^x \left (1225 x^2+245 x^3+e^{5/x} \left (-1225+245 x^2\right )\right )}{x^2} \, dx=5 \left (x+49 e^x \left (4+e^{5/x}+x\right )\right ) \]
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Time = 0.24 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.37, number of steps used = 9, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.150, Rules used = {14, 6820, 6874, 2225, 2207, 6838} \[ \int \frac {5 x^2+e^x \left (1225 x^2+245 x^3+e^{5/x} \left (-1225+245 x^2\right )\right )}{x^2} \, dx=245 e^x x+5 x+980 e^x+245 e^{x+\frac {5}{x}} \]
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Rule 14
Rule 2207
Rule 2225
Rule 6820
Rule 6838
Rule 6874
Rubi steps \begin{align*} \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{align*}
Time = 0.13 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.21 \[ \int \frac {5 x^2+e^x \left (1225 x^2+245 x^3+e^{5/x} \left (-1225+245 x^2\right )\right )}{x^2} \, dx=245 e^{\frac {5}{x}+x}+5 x+245 e^x (4+x) \]
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Time = 0.30 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.26
method | result | size |
parallelrisch | \(245 \,{\mathrm e}^{x} x +245 \,{\mathrm e}^{x} {\mathrm e}^{\frac {5}{x}}+5 x +980 \,{\mathrm e}^{x}\) | \(24\) |
risch | \(5 x +\left (980+245 x \right ) {\mathrm e}^{x}+245 \,{\mathrm e}^{\frac {x^{2}+5}{x}}\) | \(25\) |
parts | \(5 x +\frac {980 \,{\mathrm e}^{x} x +245 \,{\mathrm e}^{x} x^{2}+245 \,{\mathrm e}^{x} x \,{\mathrm e}^{\frac {5}{x}}}{x}\) | \(33\) |
norman | \(\frac {5 x^{2}+980 \,{\mathrm e}^{x} x +245 \,{\mathrm e}^{x} x^{2}+245 \,{\mathrm e}^{x} x \,{\mathrm e}^{\frac {5}{x}}}{x}\) | \(34\) |
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Time = 0.27 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {5 x^2+e^x \left (1225 x^2+245 x^3+e^{5/x} \left (-1225+245 x^2\right )\right )}{x^2} \, dx=245 \, {\left (x + e^{\frac {5}{x}} + 4\right )} e^{x} + 5 \, x \]
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Time = 1.22 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {5 x^2+e^x \left (1225 x^2+245 x^3+e^{5/x} \left (-1225+245 x^2\right )\right )}{x^2} \, dx=5 x + \left (245 x + 245 e^{\frac {5}{x}} + 980\right ) e^{x} \]
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Time = 0.24 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.32 \[ \int \frac {5 x^2+e^x \left (1225 x^2+245 x^3+e^{5/x} \left (-1225+245 x^2\right )\right )}{x^2} \, dx=245 \, {\left (x - 1\right )} e^{x} + 5 \, x + 245 \, e^{\left (x + \frac {5}{x}\right )} + 1225 \, e^{x} \]
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Time = 0.27 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.32 \[ \int \frac {5 x^2+e^x \left (1225 x^2+245 x^3+e^{5/x} \left (-1225+245 x^2\right )\right )}{x^2} \, dx=245 \, x e^{x} + 5 \, x + 980 \, e^{x} + 245 \, e^{\left (\frac {x^{2} + 5}{x}\right )} \]
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Time = 14.92 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.21 \[ \int \frac {5 x^2+e^x \left (1225 x^2+245 x^3+e^{5/x} \left (-1225+245 x^2\right )\right )}{x^2} \, dx=5\,x+245\,{\mathrm {e}}^{x+\frac {5}{x}}+980\,{\mathrm {e}}^x+245\,x\,{\mathrm {e}}^x \]
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