Integrand size = 51, antiderivative size = 19 \[ \int \left (-3 e^{3 x}+e^{2 x} \left (-2+4 e^4-4 x\right )+e^x \left (-e^8-2 x-x^2+e^4 (2+2 x)\right )\right ) \, dx=-e^x \left (e^4-e^x-x\right )^2 \]
[Out]
Leaf count is larger than twice the leaf count of optimal. \(62\) vs. \(2(19)=38\).
Time = 0.05 (sec) , antiderivative size = 62, normalized size of antiderivative = 3.26, number of steps used = 14, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {2225, 2207, 2227} \[ \int \left (-3 e^{3 x}+e^{2 x} \left (-2+4 e^4-4 x\right )+e^x \left (-e^8-2 x-x^2+e^4 (2+2 x)\right )\right ) \, dx=-e^x x^2+e^{2 x}-e^{3 x}-2 e^{x+4}-e^{x+8}+2 e^{x+4} (x+1)-e^{2 x} \left (2 x-2 e^4+1\right ) \]
[In]
[Out]
Rule 2207
Rule 2225
Rule 2227
Rubi steps \begin{align*} \text {integral}& = -\left (3 \int e^{3 x} \, dx\right )+\int e^{2 x} \left (-2+4 e^4-4 x\right ) \, dx+\int e^x \left (-e^8-2 x-x^2+e^4 (2+2 x)\right ) \, dx \\ & = -e^{3 x}-e^{2 x} \left (1-2 e^4+2 x\right )+2 \int e^{2 x} \, dx+\int \left (-e^{8+x}-2 e^x x-e^x x^2+2 e^{4+x} (1+x)\right ) \, dx \\ & = e^{2 x}-e^{3 x}-e^{2 x} \left (1-2 e^4+2 x\right )-2 \int e^x x \, dx+2 \int e^{4+x} (1+x) \, dx-\int e^{8+x} \, dx-\int e^x x^2 \, dx \\ & = e^{2 x}-e^{3 x}-e^{8+x}-2 e^x x-e^x x^2+2 e^{4+x} (1+x)-e^{2 x} \left (1-2 e^4+2 x\right )+2 \int e^x \, dx-2 \int e^{4+x} \, dx+2 \int e^x x \, dx \\ & = 2 e^x+e^{2 x}-e^{3 x}-2 e^{4+x}-e^{8+x}-e^x x^2+2 e^{4+x} (1+x)-e^{2 x} \left (1-2 e^4+2 x\right )-2 \int e^x \, dx \\ & = e^{2 x}-e^{3 x}-2 e^{4+x}-e^{8+x}-e^x x^2+2 e^{4+x} (1+x)-e^{2 x} \left (1-2 e^4+2 x\right ) \\ \end{align*}
Time = 1.86 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \left (-3 e^{3 x}+e^{2 x} \left (-2+4 e^4-4 x\right )+e^x \left (-e^8-2 x-x^2+e^4 (2+2 x)\right )\right ) \, dx=-e^x \left (-e^4+e^x+x\right )^2 \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. \(38\) vs. \(2(16)=32\).
Time = 0.50 (sec) , antiderivative size = 39, normalized size of antiderivative = 2.05
method | result | size |
risch | \(-{\mathrm e}^{3 x}+\left (2 \,{\mathrm e}^{4}-2 x \right ) {\mathrm e}^{2 x}+\left (-{\mathrm e}^{8}+2 x \,{\mathrm e}^{4}-x^{2}\right ) {\mathrm e}^{x}\) | \(39\) |
norman | \(2 x \,{\mathrm e}^{4} {\mathrm e}^{x}-{\mathrm e}^{x} x^{2}+2 \,{\mathrm e}^{2 x} {\mathrm e}^{4}-2 x \,{\mathrm e}^{2 x}-{\mathrm e}^{8} {\mathrm e}^{x}-{\mathrm e}^{3 x}\) | \(45\) |
parallelrisch | \(2 x \,{\mathrm e}^{4} {\mathrm e}^{x}-{\mathrm e}^{x} x^{2}+2 \,{\mathrm e}^{2 x} {\mathrm e}^{4}-2 x \,{\mathrm e}^{2 x}-{\mathrm e}^{8} {\mathrm e}^{x}-{\mathrm e}^{3 x}\) | \(45\) |
default | \(-2 x \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{2 x} {\mathrm e}^{4}-{\mathrm e}^{x} x^{2}+2 \,{\mathrm e}^{4} {\mathrm e}^{x}-{\mathrm e}^{8} {\mathrm e}^{x}+2 \,{\mathrm e}^{4} \left ({\mathrm e}^{x} x -{\mathrm e}^{x}\right )-{\mathrm e}^{3 x}\) | \(57\) |
parts | \(-2 x \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{2 x} {\mathrm e}^{4}-{\mathrm e}^{x} x^{2}+2 \,{\mathrm e}^{4} {\mathrm e}^{x}-{\mathrm e}^{8} {\mathrm e}^{x}+2 \,{\mathrm e}^{4} \left ({\mathrm e}^{x} x -{\mathrm e}^{x}\right )-{\mathrm e}^{3 x}\) | \(57\) |
meijerg | \(2-{\mathrm e}^{3 x}-\left (2 \,{\mathrm e}^{4}-1\right ) \left (1-{\mathrm e}^{2 x}\right )-\left (-{\mathrm e}^{8}+2 \,{\mathrm e}^{4}\right ) \left (1-{\mathrm e}^{x}\right )-\frac {\left (3 x^{2}-6 x +6\right ) {\mathrm e}^{x}}{3}+\frac {\left (-4 x +2\right ) {\mathrm e}^{2 x}}{2}-\left (-2 \,{\mathrm e}^{4}+2\right ) \left (1-\frac {\left (2-2 x \right ) {\mathrm e}^{x}}{2}\right )\) | \(86\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 34 vs. \(2 (14) = 28\).
Time = 0.24 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.79 \[ \int \left (-3 e^{3 x}+e^{2 x} \left (-2+4 e^4-4 x\right )+e^x \left (-e^8-2 x-x^2+e^4 (2+2 x)\right )\right ) \, dx=-2 \, {\left (x - e^{4}\right )} e^{\left (2 \, x\right )} - {\left (x^{2} - 2 \, x e^{4} + e^{8}\right )} e^{x} - e^{\left (3 \, x\right )} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 34 vs. \(2 (14) = 28\).
Time = 0.09 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.79 \[ \int \left (-3 e^{3 x}+e^{2 x} \left (-2+4 e^4-4 x\right )+e^x \left (-e^8-2 x-x^2+e^4 (2+2 x)\right )\right ) \, dx=\left (- 2 x + 2 e^{4}\right ) e^{2 x} + \left (- x^{2} + 2 x e^{4} - e^{8}\right ) e^{x} - e^{3 x} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (14) = 28\).
Time = 0.20 (sec) , antiderivative size = 63, normalized size of antiderivative = 3.32 \[ \int \left (-3 e^{3 x}+e^{2 x} \left (-2+4 e^4-4 x\right )+e^x \left (-e^8-2 x-x^2+e^4 (2+2 x)\right )\right ) \, dx=-2 \, {\left (x - e^{4}\right )} e^{\left (2 \, x\right )} - {\left (x^{2} - 2 \, x + 2\right )} e^{x} + 2 \, {\left (x e^{4} - e^{4}\right )} e^{x} - 2 \, {\left (x - 1\right )} e^{x} - e^{\left (3 \, x\right )} - e^{\left (x + 8\right )} + 2 \, e^{\left (x + 4\right )} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 42 vs. \(2 (14) = 28\).
Time = 0.26 (sec) , antiderivative size = 42, normalized size of antiderivative = 2.21 \[ \int \left (-3 e^{3 x}+e^{2 x} \left (-2+4 e^4-4 x\right )+e^x \left (-e^8-2 x-x^2+e^4 (2+2 x)\right )\right ) \, dx=-x^{2} e^{x} - 2 \, x e^{\left (2 \, x\right )} + 2 \, x e^{\left (x + 4\right )} - e^{\left (3 \, x\right )} + 2 \, e^{\left (2 \, x + 4\right )} - e^{\left (x + 8\right )} \]
[In]
[Out]
Time = 0.13 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \left (-3 e^{3 x}+e^{2 x} \left (-2+4 e^4-4 x\right )+e^x \left (-e^8-2 x-x^2+e^4 (2+2 x)\right )\right ) \, dx=-{\mathrm {e}}^x\,{\left (x-{\mathrm {e}}^4+{\mathrm {e}}^x\right )}^2 \]
[In]
[Out]