Integrand size = 20, antiderivative size = 23 \[ \int \frac {e^8 \left (-96-160 x-64 x^2\right )}{9 x^7} \, dx=\frac {16 e^8 \left (-3+\frac {-1+2 x}{x}\right )^2}{9 x^4} \]
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Time = 0.01 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.35, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 14} \[ \int \frac {e^8 \left (-96-160 x-64 x^2\right )}{9 x^7} \, dx=\frac {16 e^8}{9 x^6}+\frac {32 e^8}{9 x^5}+\frac {16 e^8}{9 x^4} \]
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Rule 12
Rule 14
Rubi steps \begin{align*} \text {integral}& = \frac {1}{9} e^8 \int \frac {-96-160 x-64 x^2}{x^7} \, dx \\ & = \frac {1}{9} e^8 \int \left (-\frac {96}{x^7}-\frac {160}{x^6}-\frac {64}{x^5}\right ) \, dx \\ & = \frac {16 e^8}{9 x^6}+\frac {32 e^8}{9 x^5}+\frac {16 e^8}{9 x^4} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.17 \[ \int \frac {e^8 \left (-96-160 x-64 x^2\right )}{9 x^7} \, dx=-\frac {32}{9} e^8 \left (-\frac {1}{2 x^6}-\frac {1}{x^5}-\frac {1}{2 x^4}\right ) \]
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Time = 0.07 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.78
method | result | size |
gosper | \(\frac {16 \left (x^{2}+2 x +1\right ) {\mathrm e}^{8}}{9 x^{6}}\) | \(18\) |
risch | \(\frac {{\mathrm e}^{8} \left (16 x^{2}+32 x +16\right )}{9 x^{6}}\) | \(18\) |
parallelrisch | \(\frac {{\mathrm e}^{8} \left (16 x^{2}+32 x +16\right )}{9 x^{6}}\) | \(20\) |
default | \(\frac {32 \,{\mathrm e}^{8} \left (\frac {1}{2 x^{4}}+\frac {1}{x^{5}}+\frac {1}{2 x^{6}}\right )}{9}\) | \(21\) |
norman | \(\frac {\frac {16 \,{\mathrm e}^{8}}{9}+\frac {32 x \,{\mathrm e}^{8}}{9}+\frac {16 x^{2} {\mathrm e}^{8}}{9}}{x^{6}}\) | \(28\) |
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Time = 0.24 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.65 \[ \int \frac {e^8 \left (-96-160 x-64 x^2\right )}{9 x^7} \, dx=\frac {16 \, {\left (x^{2} + 2 \, x + 1\right )} e^{8}}{9 \, x^{6}} \]
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Time = 0.12 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.17 \[ \int \frac {e^8 \left (-96-160 x-64 x^2\right )}{9 x^7} \, dx=- \frac {- 16 x^{2} e^{8} - 32 x e^{8} - 16 e^{8}}{9 x^{6}} \]
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Time = 0.19 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.65 \[ \int \frac {e^8 \left (-96-160 x-64 x^2\right )}{9 x^7} \, dx=\frac {16 \, {\left (x^{2} + 2 \, x + 1\right )} e^{8}}{9 \, x^{6}} \]
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Time = 0.26 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.65 \[ \int \frac {e^8 \left (-96-160 x-64 x^2\right )}{9 x^7} \, dx=\frac {16 \, {\left (x^{2} + 2 \, x + 1\right )} e^{8}}{9 \, x^{6}} \]
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Time = 0.05 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.96 \[ \int \frac {e^8 \left (-96-160 x-64 x^2\right )}{9 x^7} \, dx=\frac {16\,{\mathrm {e}}^8\,x^2+32\,{\mathrm {e}}^8\,x+16\,{\mathrm {e}}^8}{9\,x^6} \]
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