Integrand size = 40, antiderivative size = 22 \[ \int \frac {-24-6 x-48 x^3-3 x^4+e \left (-45-90 x^3\right )}{e \left (1-2 x^3+x^6\right )} \, dx=\frac {9 x \left (5+\frac {8+x}{3 e}\right )}{-1+x^3} \]
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Time = 0.02 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.95, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 28, 1872, 8} \[ \int \frac {-24-6 x-48 x^3-3 x^4+e \left (-45-90 x^3\right )}{e \left (1-2 x^3+x^6\right )} \, dx=-\frac {3 x (x+15 e+8)}{e \left (1-x^3\right )} \]
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Rule 8
Rule 12
Rule 28
Rule 1872
Rubi steps \begin{align*} \text {integral}& = \frac {\int \frac {-24-6 x-48 x^3-3 x^4+e \left (-45-90 x^3\right )}{1-2 x^3+x^6} \, dx}{e} \\ & = \frac {\int \frac {-24-6 x-48 x^3-3 x^4+e \left (-45-90 x^3\right )}{\left (-1+x^3\right )^2} \, dx}{e} \\ & = -\frac {3 x (8+15 e+x)}{e \left (1-x^3\right )}+\frac {\int 0 \, dx}{3 e} \\ & = -\frac {3 x (8+15 e+x)}{e \left (1-x^3\right )} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.86 \[ \int \frac {-24-6 x-48 x^3-3 x^4+e \left (-45-90 x^3\right )}{e \left (1-2 x^3+x^6\right )} \, dx=\frac {3 x (8+15 e+x)}{e \left (-1+x^3\right )} \]
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Time = 0.05 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00
method | result | size |
gosper | \(\frac {3 x \left (x +15 \,{\mathrm e}+8\right ) {\mathrm e}^{-1}}{x^{3}-1}\) | \(22\) |
risch | \(\frac {{\mathrm e}^{-1} \left (3 x^{2}+\left (24+45 \,{\mathrm e}\right ) x \right )}{x^{3}-1}\) | \(25\) |
parallelrisch | \(\frac {{\mathrm e}^{-1} \left (45 x \,{\mathrm e}+3 x^{2}+24 x \right )}{x^{3}-1}\) | \(27\) |
norman | \(\frac {3 x^{2} {\mathrm e}^{-1}+3 \left (15 \,{\mathrm e}+8\right ) {\mathrm e}^{-1} x}{x^{3}-1}\) | \(32\) |
default | \({\mathrm e}^{-1} \left (\frac {3 \left (-2-5 \,{\mathrm e}\right ) x +9+15 \,{\mathrm e}}{x^{2}+x +1}-\frac {3 \left (-5 \,{\mathrm e}-3\right )}{-1+x}\right )\) | \(44\) |
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Time = 0.26 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int \frac {-24-6 x-48 x^3-3 x^4+e \left (-45-90 x^3\right )}{e \left (1-2 x^3+x^6\right )} \, dx=\frac {3 \, {\left (x^{2} + 15 \, x e + 8 \, x\right )} e^{\left (-1\right )}}{x^{3} - 1} \]
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Time = 0.50 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.18 \[ \int \frac {-24-6 x-48 x^3-3 x^4+e \left (-45-90 x^3\right )}{e \left (1-2 x^3+x^6\right )} \, dx=- \frac {- 3 x^{2} + x \left (- 45 e - 24\right )}{e x^{3} - e} \]
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Time = 0.20 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int \frac {-24-6 x-48 x^3-3 x^4+e \left (-45-90 x^3\right )}{e \left (1-2 x^3+x^6\right )} \, dx=\frac {3 \, {\left (x^{2} + x {\left (15 \, e + 8\right )}\right )} e^{\left (-1\right )}}{x^{3} - 1} \]
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Time = 0.26 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int \frac {-24-6 x-48 x^3-3 x^4+e \left (-45-90 x^3\right )}{e \left (1-2 x^3+x^6\right )} \, dx=\frac {3 \, {\left (x^{2} + 15 \, x e + 8 \, x\right )} e^{\left (-1\right )}}{x^{3} - 1} \]
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Time = 10.06 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.27 \[ \int \frac {-24-6 x-48 x^3-3 x^4+e \left (-45-90 x^3\right )}{e \left (1-2 x^3+x^6\right )} \, dx=-\frac {3\,x^2+\left (45\,\mathrm {e}+24\right )\,x}{\mathrm {e}-x^3\,\mathrm {e}} \]
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