Integrand size = 16, antiderivative size = 22 \[ \int \frac {-4+10 x^2-2 x^3}{x^2} \, dx=-3+x+(8-x) x+\frac {4+x+x^2}{x}+\log (2) \]
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Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.64, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {14} \[ \int \frac {-4+10 x^2-2 x^3}{x^2} \, dx=-x^2+10 x+\frac {4}{x} \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (10-\frac {4}{x^2}-2 x\right ) \, dx \\ & = \frac {4}{x}+10 x-x^2 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.64 \[ \int \frac {-4+10 x^2-2 x^3}{x^2} \, dx=\frac {4}{x}+10 x-x^2 \]
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Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.68
method | result | size |
default | \(10 x -x^{2}+\frac {4}{x}\) | \(15\) |
risch | \(10 x -x^{2}+\frac {4}{x}\) | \(15\) |
gosper | \(-\frac {x^{3}-10 x^{2}-4}{x}\) | \(16\) |
parallelrisch | \(-\frac {x^{3}-10 x^{2}-4}{x}\) | \(16\) |
norman | \(\frac {-x^{3}+10 x^{2}+4}{x}\) | \(17\) |
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none
Time = 0.34 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.68 \[ \int \frac {-4+10 x^2-2 x^3}{x^2} \, dx=-\frac {x^{3} - 10 \, x^{2} - 4}{x} \]
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Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.36 \[ \int \frac {-4+10 x^2-2 x^3}{x^2} \, dx=- x^{2} + 10 x + \frac {4}{x} \]
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none
Time = 0.19 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.64 \[ \int \frac {-4+10 x^2-2 x^3}{x^2} \, dx=-x^{2} + 10 \, x + \frac {4}{x} \]
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none
Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.64 \[ \int \frac {-4+10 x^2-2 x^3}{x^2} \, dx=-x^{2} + 10 \, x + \frac {4}{x} \]
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Time = 0.03 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.73 \[ \int \frac {-4+10 x^2-2 x^3}{x^2} \, dx=\frac {-x^3+10\,x^2+4}{x} \]
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