Integrand size = 24, antiderivative size = 29 \[ \int \frac {-192+144 x+104 x^2-32 x^3-2 x^6}{x^5} \, dx=-x^2+\frac {1}{3} \left (1+4 \left (\left (-4-\frac {3 (-2+x)}{x^2}\right )^2+\log (4)\right )\right ) \]
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Time = 0.01 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.90, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {14} \[ \int \frac {-192+144 x+104 x^2-32 x^3-2 x^6}{x^5} \, dx=\frac {48}{x^4}-\frac {48}{x^3}-x^2-\frac {52}{x^2}+\frac {32}{x} \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {192}{x^5}+\frac {144}{x^4}+\frac {104}{x^3}-\frac {32}{x^2}-2 x\right ) \, dx \\ & = \frac {48}{x^4}-\frac {48}{x^3}-\frac {52}{x^2}+\frac {32}{x}-x^2 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.03 \[ \int \frac {-192+144 x+104 x^2-32 x^3-2 x^6}{x^5} \, dx=-2 \left (-\frac {24}{x^4}+\frac {24}{x^3}+\frac {26}{x^2}-\frac {16}{x}+\frac {x^2}{2}\right ) \]
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Time = 0.04 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.83
method | result | size |
gosper | \(-\frac {x^{6}-32 x^{3}+52 x^{2}+48 x -48}{x^{4}}\) | \(24\) |
parallelrisch | \(-\frac {x^{6}-32 x^{3}+52 x^{2}+48 x -48}{x^{4}}\) | \(24\) |
norman | \(\frac {-x^{6}+32 x^{3}-52 x^{2}-48 x +48}{x^{4}}\) | \(25\) |
risch | \(-x^{2}+\frac {32 x^{3}-52 x^{2}-48 x +48}{x^{4}}\) | \(26\) |
default | \(-x^{2}+\frac {48}{x^{4}}-\frac {48}{x^{3}}+\frac {32}{x}-\frac {52}{x^{2}}\) | \(27\) |
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Time = 0.24 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.79 \[ \int \frac {-192+144 x+104 x^2-32 x^3-2 x^6}{x^5} \, dx=-\frac {x^{6} - 32 \, x^{3} + 52 \, x^{2} + 48 \, x - 48}{x^{4}} \]
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Time = 0.04 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.76 \[ \int \frac {-192+144 x+104 x^2-32 x^3-2 x^6}{x^5} \, dx=- x^{2} - \frac {- 32 x^{3} + 52 x^{2} + 48 x - 48}{x^{4}} \]
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Time = 0.18 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.90 \[ \int \frac {-192+144 x+104 x^2-32 x^3-2 x^6}{x^5} \, dx=-x^{2} + \frac {4 \, {\left (8 \, x^{3} - 13 \, x^{2} - 12 \, x + 12\right )}}{x^{4}} \]
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Time = 0.28 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.90 \[ \int \frac {-192+144 x+104 x^2-32 x^3-2 x^6}{x^5} \, dx=-x^{2} + \frac {4 \, {\left (8 \, x^{3} - 13 \, x^{2} - 12 \, x + 12\right )}}{x^{4}} \]
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Time = 0.03 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.90 \[ \int \frac {-192+144 x+104 x^2-32 x^3-2 x^6}{x^5} \, dx=-x^2-\frac {-32\,x^3+52\,x^2+48\,x-48}{x^4} \]
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