Integrand size = 15, antiderivative size = 17 \[ \int \frac {1}{5} \left (1+e^3 (5+90 x)\right ) \, dx=\frac {x}{5}+e^3 \left (x+9 x^2\right ) \]
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Time = 0.00 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.18, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12} \[ \int \frac {1}{5} \left (1+e^3 (5+90 x)\right ) \, dx=\frac {1}{36} e^3 (18 x+1)^2+\frac {x}{5} \]
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Rule 12
Rubi steps \begin{align*} \text {integral}& = \frac {1}{5} \int \left (1+e^3 (5+90 x)\right ) \, dx \\ & = \frac {x}{5}+\frac {1}{36} e^3 (1+18 x)^2 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.12 \[ \int \frac {1}{5} \left (1+e^3 (5+90 x)\right ) \, dx=\frac {x}{5}+e^3 x+9 e^3 x^2 \]
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Time = 0.04 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88
method | result | size |
gosper | \(\frac {x \left (45 x \,{\mathrm e}^{3}+5 \,{\mathrm e}^{3}+1\right )}{5}\) | \(15\) |
norman | \(\left ({\mathrm e}^{3}+\frac {1}{5}\right ) x +9 x^{2} {\mathrm e}^{3}\) | \(15\) |
default | \(9 x^{2} {\mathrm e}^{3}+x \,{\mathrm e}^{3}+\frac {x}{5}\) | \(16\) |
risch | \(9 x^{2} {\mathrm e}^{3}+x \,{\mathrm e}^{3}+\frac {x}{5}\) | \(16\) |
parts | \(9 x^{2} {\mathrm e}^{3}+x \,{\mathrm e}^{3}+\frac {x}{5}\) | \(16\) |
parallelrisch | \(\frac {{\mathrm e}^{3} \left (45 x^{2}+5 x \right )}{5}+\frac {x}{5}\) | \(18\) |
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Time = 0.24 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int \frac {1}{5} \left (1+e^3 (5+90 x)\right ) \, dx={\left (9 \, x^{2} + x\right )} e^{3} + \frac {1}{5} \, x \]
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Time = 0.02 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int \frac {1}{5} \left (1+e^3 (5+90 x)\right ) \, dx=9 x^{2} e^{3} + x \left (\frac {1}{5} + e^{3}\right ) \]
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Time = 0.17 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int \frac {1}{5} \left (1+e^3 (5+90 x)\right ) \, dx={\left (9 \, x^{2} + x\right )} e^{3} + \frac {1}{5} \, x \]
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Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int \frac {1}{5} \left (1+e^3 (5+90 x)\right ) \, dx={\left (9 \, x^{2} + x\right )} e^{3} + \frac {1}{5} \, x \]
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Time = 12.16 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {1}{5} \left (1+e^3 (5+90 x)\right ) \, dx=\frac {\left (90\,x+5\right )\,\left ({\mathrm {e}}^3\,\left (90\,x+5\right )+2\right )}{900} \]
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