Integrand size = 83, antiderivative size = 29 \[ \int \frac {1}{9} \left (-9+e^{8 x} (-250-2000 x)+e^{12 x} (-96-1152 x)+e^{6 x} (-48-288 x)+e^{16 x} (-1-16 x)+e^{14 x} (16+224 x)+e^{4 x} (96+384 x)+e^{10 x} (256+2560 x)\right ) \, dx=3-\frac {1}{9} \left (3-e^{4 x} \left (4-e^{2 x}\right )^2\right )^2 x \]
[Out]
Leaf count is larger than twice the leaf count of optimal. \(165\) vs. \(2(29)=58\).
Time = 0.05 (sec) , antiderivative size = 165, normalized size of antiderivative = 5.69, number of steps used = 16, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {12, 2207, 2225} \[ \int \frac {1}{9} \left (-9+e^{8 x} (-250-2000 x)+e^{12 x} (-96-1152 x)+e^{6 x} (-48-288 x)+e^{16 x} (-1-16 x)+e^{14 x} (16+224 x)+e^{4 x} (96+384 x)+e^{10 x} (256+2560 x)\right ) \, dx=-x-\frac {8 e^{4 x}}{3}+\frac {8 e^{6 x}}{9}+\frac {125 e^{8 x}}{36}-\frac {128 e^{10 x}}{45}+\frac {8 e^{12 x}}{9}-\frac {8 e^{14 x}}{63}+\frac {e^{16 x}}{144}+\frac {8}{3} e^{4 x} (4 x+1)-\frac {8}{9} e^{6 x} (6 x+1)-\frac {125}{36} e^{8 x} (8 x+1)+\frac {128}{45} e^{10 x} (10 x+1)-\frac {8}{9} e^{12 x} (12 x+1)+\frac {8}{63} e^{14 x} (14 x+1)-\frac {1}{144} e^{16 x} (16 x+1) \]
[In]
[Out]
Rule 12
Rule 2207
Rule 2225
Rubi steps \begin{align*} \text {integral}& = \frac {1}{9} \int \left (-9+e^{8 x} (-250-2000 x)+e^{12 x} (-96-1152 x)+e^{6 x} (-48-288 x)+e^{16 x} (-1-16 x)+e^{14 x} (16+224 x)+e^{4 x} (96+384 x)+e^{10 x} (256+2560 x)\right ) \, dx \\ & = -x+\frac {1}{9} \int e^{8 x} (-250-2000 x) \, dx+\frac {1}{9} \int e^{12 x} (-96-1152 x) \, dx+\frac {1}{9} \int e^{6 x} (-48-288 x) \, dx+\frac {1}{9} \int e^{16 x} (-1-16 x) \, dx+\frac {1}{9} \int e^{14 x} (16+224 x) \, dx+\frac {1}{9} \int e^{4 x} (96+384 x) \, dx+\frac {1}{9} \int e^{10 x} (256+2560 x) \, dx \\ & = -x+\frac {8}{3} e^{4 x} (1+4 x)-\frac {8}{9} e^{6 x} (1+6 x)-\frac {125}{36} e^{8 x} (1+8 x)+\frac {128}{45} e^{10 x} (1+10 x)-\frac {8}{9} e^{12 x} (1+12 x)+\frac {8}{63} e^{14 x} (1+14 x)-\frac {1}{144} e^{16 x} (1+16 x)+\frac {1}{9} \int e^{16 x} \, dx-\frac {16}{9} \int e^{14 x} \, dx+\frac {16}{3} \int e^{6 x} \, dx-\frac {32}{3} \int e^{4 x} \, dx+\frac {32}{3} \int e^{12 x} \, dx+\frac {250}{9} \int e^{8 x} \, dx-\frac {256}{9} \int e^{10 x} \, dx \\ & = -\frac {8 e^{4 x}}{3}+\frac {8 e^{6 x}}{9}+\frac {125 e^{8 x}}{36}-\frac {128 e^{10 x}}{45}+\frac {8 e^{12 x}}{9}-\frac {8 e^{14 x}}{63}+\frac {e^{16 x}}{144}-x+\frac {8}{3} e^{4 x} (1+4 x)-\frac {8}{9} e^{6 x} (1+6 x)-\frac {125}{36} e^{8 x} (1+8 x)+\frac {128}{45} e^{10 x} (1+10 x)-\frac {8}{9} e^{12 x} (1+12 x)+\frac {8}{63} e^{14 x} (1+14 x)-\frac {1}{144} e^{16 x} (1+16 x) \\ \end{align*}
Time = 0.68 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.97 \[ \int \frac {1}{9} \left (-9+e^{8 x} (-250-2000 x)+e^{12 x} (-96-1152 x)+e^{6 x} (-48-288 x)+e^{16 x} (-1-16 x)+e^{14 x} (16+224 x)+e^{4 x} (96+384 x)+e^{10 x} (256+2560 x)\right ) \, dx=-\frac {1}{9} \left (-3+16 e^{4 x}-8 e^{6 x}+e^{8 x}\right )^2 x \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. \(53\) vs. \(2(25)=50\).
Time = 0.38 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.86
method | result | size |
default | \(-x -\frac {250 x \,{\mathrm e}^{8 x}}{9}-\frac {32 \,{\mathrm e}^{12 x} x}{3}-\frac {16 x \,{\mathrm e}^{6 x}}{3}-\frac {{\mathrm e}^{16 x} x}{9}+\frac {16 \,{\mathrm e}^{14 x} x}{9}+\frac {32 x \,{\mathrm e}^{4 x}}{3}+\frac {256 \,{\mathrm e}^{10 x} x}{9}\) | \(54\) |
risch | \(-x -\frac {250 x \,{\mathrm e}^{8 x}}{9}-\frac {32 \,{\mathrm e}^{12 x} x}{3}-\frac {16 x \,{\mathrm e}^{6 x}}{3}-\frac {{\mathrm e}^{16 x} x}{9}+\frac {16 \,{\mathrm e}^{14 x} x}{9}+\frac {32 x \,{\mathrm e}^{4 x}}{3}+\frac {256 \,{\mathrm e}^{10 x} x}{9}\) | \(54\) |
parallelrisch | \(-x -\frac {250 x \,{\mathrm e}^{8 x}}{9}-\frac {32 \,{\mathrm e}^{12 x} x}{3}-\frac {16 x \,{\mathrm e}^{6 x}}{3}-\frac {{\mathrm e}^{16 x} x}{9}+\frac {16 \,{\mathrm e}^{14 x} x}{9}+\frac {32 x \,{\mathrm e}^{4 x}}{3}+\frac {256 \,{\mathrm e}^{10 x} x}{9}\) | \(54\) |
parts | \(-x -\frac {250 x \,{\mathrm e}^{8 x}}{9}-\frac {32 \,{\mathrm e}^{12 x} x}{3}-\frac {16 x \,{\mathrm e}^{6 x}}{3}-\frac {{\mathrm e}^{16 x} x}{9}+\frac {16 \,{\mathrm e}^{14 x} x}{9}+\frac {32 x \,{\mathrm e}^{4 x}}{3}+\frac {256 \,{\mathrm e}^{10 x} x}{9}\) | \(54\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (22) = 44\).
Time = 0.25 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.83 \[ \int \frac {1}{9} \left (-9+e^{8 x} (-250-2000 x)+e^{12 x} (-96-1152 x)+e^{6 x} (-48-288 x)+e^{16 x} (-1-16 x)+e^{14 x} (16+224 x)+e^{4 x} (96+384 x)+e^{10 x} (256+2560 x)\right ) \, dx=-\frac {1}{9} \, x e^{\left (16 \, x\right )} + \frac {16}{9} \, x e^{\left (14 \, x\right )} - \frac {32}{3} \, x e^{\left (12 \, x\right )} + \frac {256}{9} \, x e^{\left (10 \, x\right )} - \frac {250}{9} \, x e^{\left (8 \, x\right )} - \frac {16}{3} \, x e^{\left (6 \, x\right )} + \frac {32}{3} \, x e^{\left (4 \, x\right )} - x \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (20) = 40\).
Time = 0.12 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.41 \[ \int \frac {1}{9} \left (-9+e^{8 x} (-250-2000 x)+e^{12 x} (-96-1152 x)+e^{6 x} (-48-288 x)+e^{16 x} (-1-16 x)+e^{14 x} (16+224 x)+e^{4 x} (96+384 x)+e^{10 x} (256+2560 x)\right ) \, dx=- \frac {x e^{16 x}}{9} + \frac {16 x e^{14 x}}{9} - \frac {32 x e^{12 x}}{3} + \frac {256 x e^{10 x}}{9} - \frac {250 x e^{8 x}}{9} - \frac {16 x e^{6 x}}{3} + \frac {32 x e^{4 x}}{3} - x \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (22) = 44\).
Time = 0.20 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.17 \[ \int \frac {1}{9} \left (-9+e^{8 x} (-250-2000 x)+e^{12 x} (-96-1152 x)+e^{6 x} (-48-288 x)+e^{16 x} (-1-16 x)+e^{14 x} (16+224 x)+e^{4 x} (96+384 x)+e^{10 x} (256+2560 x)\right ) \, dx=-\frac {1}{9} \, x e^{\left (16 \, x\right )} + \frac {16}{9} \, x e^{\left (14 \, x\right )} - \frac {32}{3} \, x e^{\left (12 \, x\right )} + \frac {256}{9} \, x e^{\left (10 \, x\right )} - \frac {250}{9} \, x e^{\left (8 \, x\right )} - \frac {16}{3} \, x e^{\left (6 \, x\right )} + \frac {8}{3} \, {\left (4 \, x - 1\right )} e^{\left (4 \, x\right )} - x + \frac {8}{3} \, e^{\left (4 \, x\right )} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 53 vs. \(2 (22) = 44\).
Time = 0.25 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.83 \[ \int \frac {1}{9} \left (-9+e^{8 x} (-250-2000 x)+e^{12 x} (-96-1152 x)+e^{6 x} (-48-288 x)+e^{16 x} (-1-16 x)+e^{14 x} (16+224 x)+e^{4 x} (96+384 x)+e^{10 x} (256+2560 x)\right ) \, dx=-\frac {1}{9} \, x e^{\left (16 \, x\right )} + \frac {16}{9} \, x e^{\left (14 \, x\right )} - \frac {32}{3} \, x e^{\left (12 \, x\right )} + \frac {256}{9} \, x e^{\left (10 \, x\right )} - \frac {250}{9} \, x e^{\left (8 \, x\right )} - \frac {16}{3} \, x e^{\left (6 \, x\right )} + \frac {32}{3} \, x e^{\left (4 \, x\right )} - x \]
[In]
[Out]
Time = 9.79 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.79 \[ \int \frac {1}{9} \left (-9+e^{8 x} (-250-2000 x)+e^{12 x} (-96-1152 x)+e^{6 x} (-48-288 x)+e^{16 x} (-1-16 x)+e^{14 x} (16+224 x)+e^{4 x} (96+384 x)+e^{10 x} (256+2560 x)\right ) \, dx=-\frac {x\,{\left (16\,{\mathrm {e}}^{4\,x}-8\,{\mathrm {e}}^{6\,x}+{\mathrm {e}}^{8\,x}-3\right )}^2}{9} \]
[In]
[Out]