Integrand size = 21, antiderivative size = 26 \[ \int \left (-3+30 x-12 x^2+e^{3 x} (1+3 x)\right ) \, dx=-6+e^2-x \left (3-e^{3 x}+x-4 (4-x) x\right ) \]
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Time = 0.01 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.42, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {2207, 2225} \[ \int \left (-3+30 x-12 x^2+e^{3 x} (1+3 x)\right ) \, dx=-4 x^3+15 x^2-3 x-\frac {e^{3 x}}{3}+\frac {1}{3} e^{3 x} (3 x+1) \]
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Rule 2207
Rule 2225
Rubi steps \begin{align*} \text {integral}& = -3 x+15 x^2-4 x^3+\int e^{3 x} (1+3 x) \, dx \\ & = -3 x+15 x^2-4 x^3+\frac {1}{3} e^{3 x} (1+3 x)-\int e^{3 x} \, dx \\ & = -\frac {e^{3 x}}{3}-3 x+15 x^2-4 x^3+\frac {1}{3} e^{3 x} (1+3 x) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.81 \[ \int \left (-3+30 x-12 x^2+e^{3 x} (1+3 x)\right ) \, dx=-3 x+e^{3 x} x+15 x^2-4 x^3 \]
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Time = 0.44 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.81
method | result | size |
derivativedivides | \(-3 x +15 x^{2}-4 x^{3}+x \,{\mathrm e}^{3 x}\) | \(21\) |
default | \(-3 x +15 x^{2}-4 x^{3}+x \,{\mathrm e}^{3 x}\) | \(21\) |
norman | \(-3 x +15 x^{2}-4 x^{3}+x \,{\mathrm e}^{3 x}\) | \(21\) |
risch | \(-3 x +15 x^{2}-4 x^{3}+x \,{\mathrm e}^{3 x}\) | \(21\) |
parallelrisch | \(-3 x +15 x^{2}-4 x^{3}+x \,{\mathrm e}^{3 x}\) | \(21\) |
parts | \(-3 x +15 x^{2}-4 x^{3}+x \,{\mathrm e}^{3 x}\) | \(21\) |
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Time = 0.27 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.77 \[ \int \left (-3+30 x-12 x^2+e^{3 x} (1+3 x)\right ) \, dx=-4 \, x^{3} + 15 \, x^{2} + x e^{\left (3 \, x\right )} - 3 \, x \]
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Time = 0.05 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.73 \[ \int \left (-3+30 x-12 x^2+e^{3 x} (1+3 x)\right ) \, dx=- 4 x^{3} + 15 x^{2} + x e^{3 x} - 3 x \]
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none
Time = 0.19 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.77 \[ \int \left (-3+30 x-12 x^2+e^{3 x} (1+3 x)\right ) \, dx=-4 \, x^{3} + 15 \, x^{2} + x e^{\left (3 \, x\right )} - 3 \, x \]
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Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.77 \[ \int \left (-3+30 x-12 x^2+e^{3 x} (1+3 x)\right ) \, dx=-4 \, x^{3} + 15 \, x^{2} + x e^{\left (3 \, x\right )} - 3 \, x \]
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Time = 0.05 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.62 \[ \int \left (-3+30 x-12 x^2+e^{3 x} (1+3 x)\right ) \, dx=x\,\left (15\,x+{\mathrm {e}}^{3\,x}-4\,x^2-3\right ) \]
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