Integrand size = 48, antiderivative size = 22 \[ \int \frac {15\ 2^{1-2 e^{e^2}} e^{e^2} \left (6-2 e^6-3 x\right )^{2 e^{e^2}}}{-6+2 e^6+3 x} \, dx=5 \left (3-e^6-\frac {3 x}{2}\right )^{2 e^{e^2}} \]
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Time = 0.01 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.45, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {12, 21, 32} \[ \int \frac {15\ 2^{1-2 e^{e^2}} e^{e^2} \left (6-2 e^6-3 x\right )^{2 e^{e^2}}}{-6+2 e^6+3 x} \, dx=5\ 4^{-e^{e^2}} \left (2 \left (3-e^6\right )-3 x\right )^{2 e^{e^2}} \]
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Rule 12
Rule 21
Rule 32
Rubi steps \begin{align*} \text {integral}& = \left (15\ 2^{1-2 e^{e^2}} e^{e^2}\right ) \int \frac {\left (6-2 e^6-3 x\right )^{2 e^{e^2}}}{-6+2 e^6+3 x} \, dx \\ & = -\left (\left (15\ 2^{1-2 e^{e^2}} e^{e^2}\right ) \int \left (6-2 e^6-3 x\right )^{-1+2 e^{e^2}} \, dx\right ) \\ & = 5\ 4^{-e^{e^2}} \left (2 \left (3-e^6\right )-3 x\right )^{2 e^{e^2}} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {15\ 2^{1-2 e^{e^2}} e^{e^2} \left (6-2 e^6-3 x\right )^{2 e^{e^2}}}{-6+2 e^6+3 x} \, dx=5 \left (3-e^6-\frac {3 x}{2}\right )^{2 e^{e^2}} \]
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Time = 0.60 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82
method | result | size |
risch | \(5 \left (-{\mathrm e}^{6}-\frac {3 x}{2}+3\right )^{2 \,{\mathrm e}^{{\mathrm e}^{2}}}\) | \(18\) |
gosper | \(5 \,{\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{2}} \ln \left (-{\mathrm e}^{6}-\frac {3 x}{2}+3\right )}\) | \(20\) |
derivativedivides | \(5 \,{\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{2}} \ln \left (-{\mathrm e}^{6}-\frac {3 x}{2}+3\right )}\) | \(20\) |
default | \(5 \,{\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{2}} \ln \left (-{\mathrm e}^{6}-\frac {3 x}{2}+3\right )}\) | \(20\) |
norman | \(5 \,{\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{2}} \ln \left (-{\mathrm e}^{6}-\frac {3 x}{2}+3\right )}\) | \(20\) |
parallelrisch | \(5 \,{\mathrm e}^{2 \,{\mathrm e}^{{\mathrm e}^{2}} \ln \left (-{\mathrm e}^{6}-\frac {3 x}{2}+3\right )}\) | \(20\) |
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none
Time = 0.24 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.77 \[ \int \frac {15\ 2^{1-2 e^{e^2}} e^{e^2} \left (6-2 e^6-3 x\right )^{2 e^{e^2}}}{-6+2 e^6+3 x} \, dx=5 \, {\left (-\frac {3}{2} \, x - e^{6} + 3\right )}^{2 \, e^{\left (e^{2}\right )}} \]
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Exception generated. \[ \int \frac {15\ 2^{1-2 e^{e^2}} e^{e^2} \left (6-2 e^6-3 x\right )^{2 e^{e^2}}}{-6+2 e^6+3 x} \, dx=\text {Exception raised: TypeError} \]
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none
Time = 0.28 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.18 \[ \int \frac {15\ 2^{1-2 e^{e^2}} e^{e^2} \left (6-2 e^6-3 x\right )^{2 e^{e^2}}}{-6+2 e^6+3 x} \, dx=\frac {5 \, {\left (-3 \, x - 2 \, e^{6} + 6\right )}^{2 \, e^{\left (e^{2}\right )}}}{2^{2 \, e^{\left (e^{2}\right )}}} \]
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\[ \int \frac {15\ 2^{1-2 e^{e^2}} e^{e^2} \left (6-2 e^6-3 x\right )^{2 e^{e^2}}}{-6+2 e^6+3 x} \, dx=\int { \frac {30 \, {\left (-\frac {3}{2} \, x - e^{6} + 3\right )}^{2 \, e^{\left (e^{2}\right )}} e^{\left (e^{2}\right )}}{3 \, x + 2 \, e^{6} - 6} \,d x } \]
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Time = 0.36 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.77 \[ \int \frac {15\ 2^{1-2 e^{e^2}} e^{e^2} \left (6-2 e^6-3 x\right )^{2 e^{e^2}}}{-6+2 e^6+3 x} \, dx=5\,{\left (3-{\mathrm {e}}^6-\frac {3\,x}{2}\right )}^{2\,{\mathrm {e}}^{{\mathrm {e}}^2}} \]
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