Integrand size = 39, antiderivative size = 17 \[ \int \frac {e^{256+x} \left (342 x+171 x^2-81 x^4+81 x^5\right )}{361+342 x^3+81 x^6} \, dx=\frac {e^{256+x}}{\frac {19}{9 x^2}+x} \]
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Time = 0.04 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.59, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.051, Rules used = {28, 2326} \[ \int \frac {e^{256+x} \left (342 x+171 x^2-81 x^4+81 x^5\right )}{361+342 x^3+81 x^6} \, dx=\frac {9 e^{x+256} \left (9 x^5+19 x^2\right )}{\left (9 x^3+19\right )^2} \]
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Rule 28
Rule 2326
Rubi steps \begin{align*} \text {integral}& = 81 \int \frac {e^{256+x} \left (342 x+171 x^2-81 x^4+81 x^5\right )}{\left (171+81 x^3\right )^2} \, dx \\ & = \frac {9 e^{256+x} \left (19 x^2+9 x^5\right )}{\left (19+9 x^3\right )^2} \\ \end{align*}
Time = 0.24 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.12 \[ \int \frac {e^{256+x} \left (342 x+171 x^2-81 x^4+81 x^5\right )}{361+342 x^3+81 x^6} \, dx=\frac {9 e^{256+x} x^2}{19+9 x^3} \]
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Time = 1.62 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.12
method | result | size |
gosper | \(\frac {9 x^{2} {\mathrm e}^{256+x}}{9 x^{3}+19}\) | \(19\) |
norman | \(\frac {9 x^{2} {\mathrm e}^{256+x}}{9 x^{3}+19}\) | \(19\) |
risch | \(\frac {9 x^{2} {\mathrm e}^{256+x}}{9 x^{3}+19}\) | \(19\) |
parallelrisch | \(\frac {9 x^{2} {\mathrm e}^{256+x}}{9 x^{3}+19}\) | \(19\) |
derivativedivides | \(\text {Expression too large to display}\) | \(520\) |
default | \(\text {Expression too large to display}\) | \(520\) |
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Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {e^{256+x} \left (342 x+171 x^2-81 x^4+81 x^5\right )}{361+342 x^3+81 x^6} \, dx=\frac {9 \, x^{2} e^{\left (x + 256\right )}}{9 \, x^{3} + 19} \]
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Time = 0.07 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int \frac {e^{256+x} \left (342 x+171 x^2-81 x^4+81 x^5\right )}{361+342 x^3+81 x^6} \, dx=\frac {9 x^{2} e^{x + 256}}{9 x^{3} + 19} \]
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Time = 0.31 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {e^{256+x} \left (342 x+171 x^2-81 x^4+81 x^5\right )}{361+342 x^3+81 x^6} \, dx=\frac {9 \, x^{2} e^{\left (x + 256\right )}}{9 \, x^{3} + 19} \]
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Time = 0.27 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {e^{256+x} \left (342 x+171 x^2-81 x^4+81 x^5\right )}{361+342 x^3+81 x^6} \, dx=\frac {9 \, x^{2} e^{\left (x + 256\right )}}{9 \, x^{3} + 19} \]
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Time = 10.04 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {e^{256+x} \left (342 x+171 x^2-81 x^4+81 x^5\right )}{361+342 x^3+81 x^6} \, dx=\frac {9\,x^2\,{\mathrm {e}}^{256}\,{\mathrm {e}}^x}{9\,x^3+19} \]
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