Integrand size = 30, antiderivative size = 23 \[ \int \left (1+e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right )\right ) \, dx=5-e-e^{3 x+\left (2+4 x^2\right )^2}+x \]
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Time = 0.03 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {6838} \[ \int \left (1+e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right )\right ) \, dx=x-e^{16 x^4+16 x^2+3 x+4} \]
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Rule 6838
Rubi steps \begin{align*} \text {integral}& = x+\int e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right ) \, dx \\ & = -e^{4+3 x+16 x^2+16 x^4}+x \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91 \[ \int \left (1+e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right )\right ) \, dx=-e^{4+3 x+16 x^2+16 x^4}+x \]
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Time = 0.09 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91
method | result | size |
default | \(x -{\mathrm e}^{16 x^{4}+16 x^{2}+3 x +4}\) | \(21\) |
norman | \(x -{\mathrm e}^{16 x^{4}+16 x^{2}+3 x +4}\) | \(21\) |
risch | \(x -{\mathrm e}^{16 x^{4}+16 x^{2}+3 x +4}\) | \(21\) |
parallelrisch | \(x -{\mathrm e}^{16 x^{4}+16 x^{2}+3 x +4}\) | \(21\) |
parts | \(x -{\mathrm e}^{16 x^{4}+16 x^{2}+3 x +4}\) | \(21\) |
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none
Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \left (1+e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right )\right ) \, dx=x - e^{\left (16 \, x^{4} + 16 \, x^{2} + 3 \, x + 4\right )} \]
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Time = 0.06 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.74 \[ \int \left (1+e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right )\right ) \, dx=x - e^{16 x^{4} + 16 x^{2} + 3 x + 4} \]
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none
Time = 0.18 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \left (1+e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right )\right ) \, dx=x - e^{\left (16 \, x^{4} + 16 \, x^{2} + 3 \, x + 4\right )} \]
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none
Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \left (1+e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right )\right ) \, dx=x - e^{\left (16 \, x^{4} + 16 \, x^{2} + 3 \, x + 4\right )} \]
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Time = 9.42 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.96 \[ \int \left (1+e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right )\right ) \, dx=x-{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^4\,{\mathrm {e}}^{16\,x^2}\,{\mathrm {e}}^{16\,x^4} \]
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