Integrand size = 22, antiderivative size = 29 \[ \int \frac {1}{3} \left (-7-e+3 e^2+6 x-9 x^2\right ) \, dx=2 e^4-x \left (1-e^2+\frac {4+e}{3}-x+x^2\right ) \]
[Out]
Time = 0.01 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.76, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {12} \[ \int \frac {1}{3} \left (-7-e+3 e^2+6 x-9 x^2\right ) \, dx=-x^3+x^2-\frac {1}{3} \left (7+e-3 e^2\right ) x \]
[In]
[Out]
Rule 12
Rubi steps \begin{align*} \text {integral}& = \frac {1}{3} \int \left (-7-e+3 e^2+6 x-9 x^2\right ) \, dx \\ & = -\frac {1}{3} \left (7+e-3 e^2\right ) x+x^2-x^3 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.86 \[ \int \frac {1}{3} \left (-7-e+3 e^2+6 x-9 x^2\right ) \, dx=-\frac {7 x}{3}-\frac {e x}{3}+e^2 x+x^2-x^3 \]
[In]
[Out]
Time = 0.35 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.69
method | result | size |
norman | \(x^{2}+\left ({\mathrm e}^{2}-\frac {{\mathrm e}}{3}-\frac {7}{3}\right ) x -x^{3}\) | \(20\) |
parallelrisch | \(x^{2}+\left ({\mathrm e}^{2}-\frac {{\mathrm e}}{3}-\frac {7}{3}\right ) x -x^{3}\) | \(20\) |
gosper | \(\frac {x \left (-3 x^{2}+3 \,{\mathrm e}^{2}-{\mathrm e}+3 x -7\right )}{3}\) | \(22\) |
default | \(-x^{3}+{\mathrm e}^{2} x -\frac {x \,{\mathrm e}}{3}+x^{2}-\frac {7 x}{3}\) | \(22\) |
risch | \(-x^{3}+{\mathrm e}^{2} x -\frac {x \,{\mathrm e}}{3}+x^{2}-\frac {7 x}{3}\) | \(22\) |
parts | \(-x^{3}+{\mathrm e}^{2} x -\frac {x \,{\mathrm e}}{3}+x^{2}-\frac {7 x}{3}\) | \(22\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.72 \[ \int \frac {1}{3} \left (-7-e+3 e^2+6 x-9 x^2\right ) \, dx=-x^{3} + x^{2} + x e^{2} - \frac {1}{3} \, x e - \frac {7}{3} \, x \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.66 \[ \int \frac {1}{3} \left (-7-e+3 e^2+6 x-9 x^2\right ) \, dx=- x^{3} + x^{2} + x \left (- \frac {7}{3} - \frac {e}{3} + e^{2}\right ) \]
[In]
[Out]
none
Time = 0.18 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.72 \[ \int \frac {1}{3} \left (-7-e+3 e^2+6 x-9 x^2\right ) \, dx=-x^{3} + x^{2} + x e^{2} - \frac {1}{3} \, x e - \frac {7}{3} \, x \]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.72 \[ \int \frac {1}{3} \left (-7-e+3 e^2+6 x-9 x^2\right ) \, dx=-x^{3} + x^{2} + x e^{2} - \frac {1}{3} \, x e - \frac {7}{3} \, x \]
[In]
[Out]
Time = 8.74 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.76 \[ \int \frac {1}{3} \left (-7-e+3 e^2+6 x-9 x^2\right ) \, dx=-x^3+x^2+\left ({\mathrm {e}}^2-\frac {\mathrm {e}}{3}-\frac {7}{3}\right )\,x \]
[In]
[Out]