Integrand size = 21, antiderivative size = 21 \[ \int \left (3+e^{2+e^3}+e^x (-1-x)-2 x\right ) \, dx=-4+\left (3+e^{2+e^3}-e^x-x\right ) x \]
[Out]
Time = 0.01 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.33, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {2207, 2225} \[ \int \left (3+e^{2+e^3}+e^x (-1-x)-2 x\right ) \, dx=-x^2+\left (3+e^{2+e^3}\right ) x+e^x-e^x (x+1) \]
[In]
[Out]
Rule 2207
Rule 2225
Rubi steps \begin{align*} \text {integral}& = \left (3+e^{2+e^3}\right ) x-x^2+\int e^x (-1-x) \, dx \\ & = \left (3+e^{2+e^3}\right ) x-x^2-e^x (1+x)+\int e^x \, dx \\ & = e^x+\left (3+e^{2+e^3}\right ) x-x^2-e^x (1+x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.14 \[ \int \left (3+e^{2+e^3}+e^x (-1-x)-2 x\right ) \, dx=3 x+e^{2+e^3} x-e^x x-x^2 \]
[In]
[Out]
Time = 0.14 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00
method | result | size |
parallelrisch | \(-{\mathrm e}^{x} x -x^{2}+\left ({\mathrm e}^{2+{\mathrm e}^{3}}+3\right ) x\) | \(21\) |
default | \(-{\mathrm e}^{x} x +3 x -x^{2}+x \,{\mathrm e}^{2+{\mathrm e}^{3}}\) | \(22\) |
norman | \(\left ({\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{3}}+3\right ) x -x^{2}-{\mathrm e}^{x} x\) | \(22\) |
risch | \(-{\mathrm e}^{x} x +3 x -x^{2}+x \,{\mathrm e}^{2+{\mathrm e}^{3}}\) | \(22\) |
parts | \(-{\mathrm e}^{x} x +3 x -x^{2}+x \,{\mathrm e}^{2+{\mathrm e}^{3}}\) | \(22\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int \left (3+e^{2+e^3}+e^x (-1-x)-2 x\right ) \, dx=-x^{2} - x e^{x} + x e^{\left (e^{3} + 2\right )} + 3 \, x \]
[In]
[Out]
Time = 0.07 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \left (3+e^{2+e^3}+e^x (-1-x)-2 x\right ) \, dx=- x^{2} - x e^{x} + x \left (3 + e^{2} e^{e^{3}}\right ) \]
[In]
[Out]
none
Time = 0.18 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int \left (3+e^{2+e^3}+e^x (-1-x)-2 x\right ) \, dx=-x^{2} - x e^{x} + x e^{\left (e^{3} + 2\right )} + 3 \, x \]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int \left (3+e^{2+e^3}+e^x (-1-x)-2 x\right ) \, dx=-x^{2} - x e^{x} + x e^{\left (e^{3} + 2\right )} + 3 \, x \]
[In]
[Out]
Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.71 \[ \int \left (3+e^{2+e^3}+e^x (-1-x)-2 x\right ) \, dx=-x\,\left (x-{\mathrm {e}}^{{\mathrm {e}}^3+2}+{\mathrm {e}}^x-3\right ) \]
[In]
[Out]