Integrand size = 22, antiderivative size = 18 \[ \int \left (2 e^{2 x}-96 e^{3 x}+6 e^{6 x}\right ) \, dx=2+e^{2 x}+\left (16-e^{3 x}\right )^2 \]
[Out]
Time = 0.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {2225} \[ \int \left (2 e^{2 x}-96 e^{3 x}+6 e^{6 x}\right ) \, dx=e^{2 x}-32 e^{3 x}+e^{6 x} \]
[In]
[Out]
Rule 2225
Rubi steps \begin{align*} \text {integral}& = 2 \int e^{2 x} \, dx+6 \int e^{6 x} \, dx-96 \int e^{3 x} \, dx \\ & = e^{2 x}-32 e^{3 x}+e^{6 x} \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \left (2 e^{2 x}-96 e^{3 x}+6 e^{6 x}\right ) \, dx=e^{2 x} \left (1-32 e^x+e^{4 x}\right ) \]
[In]
[Out]
Time = 0.04 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.89
method | result | size |
norman | \({\mathrm e}^{6 x}-32 \,{\mathrm e}^{3 x}+{\mathrm e}^{2 x}\) | \(16\) |
risch | \({\mathrm e}^{6 x}-32 \,{\mathrm e}^{3 x}+{\mathrm e}^{2 x}\) | \(16\) |
meijerg | \(30+{\mathrm e}^{6 x}-32 \,{\mathrm e}^{3 x}+{\mathrm e}^{2 x}\) | \(17\) |
default | \({\mathrm e}^{6 x}-32 \,{\mathrm e}^{3 x}+{\mathrm e}^{2 x}\) | \(18\) |
parallelrisch | \({\mathrm e}^{6 x}-32 \,{\mathrm e}^{3 x}+{\mathrm e}^{2 x}\) | \(18\) |
parts | \({\mathrm e}^{6 x}-32 \,{\mathrm e}^{3 x}+{\mathrm e}^{2 x}\) | \(18\) |
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \left (2 e^{2 x}-96 e^{3 x}+6 e^{6 x}\right ) \, dx=e^{\left (6 \, x\right )} - 32 \, e^{\left (3 \, x\right )} + e^{\left (2 \, x\right )} \]
[In]
[Out]
Time = 0.05 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \left (2 e^{2 x}-96 e^{3 x}+6 e^{6 x}\right ) \, dx=e^{6 x} - 32 e^{3 x} + e^{2 x} \]
[In]
[Out]
none
Time = 0.17 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \left (2 e^{2 x}-96 e^{3 x}+6 e^{6 x}\right ) \, dx=e^{\left (6 \, x\right )} - 32 \, e^{\left (3 \, x\right )} + e^{\left (2 \, x\right )} \]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \left (2 e^{2 x}-96 e^{3 x}+6 e^{6 x}\right ) \, dx=e^{\left (6 \, x\right )} - 32 \, e^{\left (3 \, x\right )} + e^{\left (2 \, x\right )} \]
[In]
[Out]
Time = 0.07 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \left (2 e^{2 x}-96 e^{3 x}+6 e^{6 x}\right ) \, dx={\mathrm {e}}^{2\,x}\,\left ({\mathrm {e}}^{4\,x}-32\,{\mathrm {e}}^x+1\right ) \]
[In]
[Out]