Integrand size = 39, antiderivative size = 33 \[ \int \frac {7442-3904 x+3278 x^3-4590 x^4+2496 x^5-1408 x^6+320 x^7-96 x^8}{x^3} \, dx=5 e^3-2 x+x^2-\frac {\left (3-4 \left (4-x+x^2\right )^2\right )^2}{x^2} \]
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Time = 0.01 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.18, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {14} \[ \int \frac {7442-3904 x+3278 x^3-4590 x^4+2496 x^5-1408 x^6+320 x^7-96 x^8}{x^3} \, dx=-16 x^6+64 x^5-352 x^4+832 x^3-2295 x^2-\frac {3721}{x^2}+3278 x+\frac {3904}{x} \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (3278+\frac {7442}{x^3}-\frac {3904}{x^2}-4590 x+2496 x^2-1408 x^3+320 x^4-96 x^5\right ) \, dx \\ & = -\frac {3721}{x^2}+\frac {3904}{x}+3278 x-2295 x^2+832 x^3-352 x^4+64 x^5-16 x^6 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.18 \[ \int \frac {7442-3904 x+3278 x^3-4590 x^4+2496 x^5-1408 x^6+320 x^7-96 x^8}{x^3} \, dx=-\frac {3721}{x^2}+\frac {3904}{x}+3278 x-2295 x^2+832 x^3-352 x^4+64 x^5-16 x^6 \]
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Time = 0.05 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.18
method | result | size |
risch | \(-16 x^{6}+64 x^{5}-352 x^{4}+832 x^{3}-2295 x^{2}+3278 x +\frac {3904 x -3721}{x^{2}}\) | \(39\) |
default | \(-16 x^{6}+64 x^{5}-352 x^{4}+832 x^{3}-2295 x^{2}+3278 x +\frac {3904}{x}-\frac {3721}{x^{2}}\) | \(40\) |
norman | \(\frac {-16 x^{8}+64 x^{7}-352 x^{6}+832 x^{5}-2295 x^{4}+3278 x^{3}+3904 x -3721}{x^{2}}\) | \(40\) |
gosper | \(-\frac {16 x^{8}-64 x^{7}+352 x^{6}-832 x^{5}+2295 x^{4}-3278 x^{3}-3904 x +3721}{x^{2}}\) | \(41\) |
parallelrisch | \(-\frac {16 x^{8}-64 x^{7}+352 x^{6}-832 x^{5}+2295 x^{4}-3278 x^{3}-3904 x +3721}{x^{2}}\) | \(41\) |
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Time = 0.24 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.21 \[ \int \frac {7442-3904 x+3278 x^3-4590 x^4+2496 x^5-1408 x^6+320 x^7-96 x^8}{x^3} \, dx=-\frac {16 \, x^{8} - 64 \, x^{7} + 352 \, x^{6} - 832 \, x^{5} + 2295 \, x^{4} - 3278 \, x^{3} - 3904 \, x + 3721}{x^{2}} \]
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Time = 0.03 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.09 \[ \int \frac {7442-3904 x+3278 x^3-4590 x^4+2496 x^5-1408 x^6+320 x^7-96 x^8}{x^3} \, dx=- 16 x^{6} + 64 x^{5} - 352 x^{4} + 832 x^{3} - 2295 x^{2} + 3278 x - \frac {3721 - 3904 x}{x^{2}} \]
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Time = 0.19 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.18 \[ \int \frac {7442-3904 x+3278 x^3-4590 x^4+2496 x^5-1408 x^6+320 x^7-96 x^8}{x^3} \, dx=-16 \, x^{6} + 64 \, x^{5} - 352 \, x^{4} + 832 \, x^{3} - 2295 \, x^{2} + 3278 \, x + \frac {61 \, {\left (64 \, x - 61\right )}}{x^{2}} \]
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Time = 0.25 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.18 \[ \int \frac {7442-3904 x+3278 x^3-4590 x^4+2496 x^5-1408 x^6+320 x^7-96 x^8}{x^3} \, dx=-16 \, x^{6} + 64 \, x^{5} - 352 \, x^{4} + 832 \, x^{3} - 2295 \, x^{2} + 3278 \, x + \frac {61 \, {\left (64 \, x - 61\right )}}{x^{2}} \]
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Time = 11.37 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.15 \[ \int \frac {7442-3904 x+3278 x^3-4590 x^4+2496 x^5-1408 x^6+320 x^7-96 x^8}{x^3} \, dx=3278\,x+\frac {3904\,x-3721}{x^2}-2295\,x^2+832\,x^3-352\,x^4+64\,x^5-16\,x^6 \]
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