Integrand size = 30, antiderivative size = 17 \[ \int \frac {150+e^x (12-2 x)-60 x+6 x^2}{25-10 x+x^2} \, dx=2 \left (-2-\frac {e^x}{-5+x}+3 x\right ) \]
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Time = 0.05 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {27, 6820, 2228} \[ \int \frac {150+e^x (12-2 x)-60 x+6 x^2}{25-10 x+x^2} \, dx=6 x+\frac {2 e^x}{5-x} \]
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Rule 27
Rule 2228
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {150+e^x (12-2 x)-60 x+6 x^2}{(-5+x)^2} \, dx \\ & = \int \left (6-\frac {2 e^x (-6+x)}{(-5+x)^2}\right ) \, dx \\ & = 6 x-2 \int \frac {e^x (-6+x)}{(-5+x)^2} \, dx \\ & = \frac {2 e^x}{5-x}+6 x \\ \end{align*}
Time = 0.16 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int \frac {150+e^x (12-2 x)-60 x+6 x^2}{25-10 x+x^2} \, dx=-\frac {2 e^x}{-5+x}+6 x \]
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Time = 0.39 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82
method | result | size |
default | \(6 x -\frac {2 \,{\mathrm e}^{x}}{-5+x}\) | \(14\) |
risch | \(6 x -\frac {2 \,{\mathrm e}^{x}}{-5+x}\) | \(14\) |
parts | \(6 x -\frac {2 \,{\mathrm e}^{x}}{-5+x}\) | \(14\) |
norman | \(\frac {6 x^{2}-2 \,{\mathrm e}^{x}-150}{-5+x}\) | \(18\) |
parallelrisch | \(\frac {6 x^{2}-2 \,{\mathrm e}^{x}-150}{-5+x}\) | \(18\) |
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Time = 0.24 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.18 \[ \int \frac {150+e^x (12-2 x)-60 x+6 x^2}{25-10 x+x^2} \, dx=\frac {2 \, {\left (3 \, x^{2} - 15 \, x - e^{x}\right )}}{x - 5} \]
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Time = 0.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.59 \[ \int \frac {150+e^x (12-2 x)-60 x+6 x^2}{25-10 x+x^2} \, dx=6 x - \frac {2 e^{x}}{x - 5} \]
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\[ \int \frac {150+e^x (12-2 x)-60 x+6 x^2}{25-10 x+x^2} \, dx=\int { \frac {2 \, {\left (3 \, x^{2} - {\left (x - 6\right )} e^{x} - 30 \, x + 75\right )}}{x^{2} - 10 \, x + 25} \,d x } \]
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none
Time = 0.27 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.18 \[ \int \frac {150+e^x (12-2 x)-60 x+6 x^2}{25-10 x+x^2} \, dx=\frac {2 \, {\left (3 \, x^{2} - 15 \, x - e^{x}\right )}}{x - 5} \]
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Time = 12.46 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.76 \[ \int \frac {150+e^x (12-2 x)-60 x+6 x^2}{25-10 x+x^2} \, dx=6\,x-\frac {2\,{\mathrm {e}}^x}{x-5} \]
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