Integrand size = 18, antiderivative size = 18 \[ \int \left (2 x+e^x \left (-91-95 x-2 x^2\right )\right ) \, dx=e+x \left (x-e^x (81+2 (5+x))\right ) \]
[Out]
Time = 0.05 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 9, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {2227, 2225, 2207} \[ \int \left (2 x+e^x \left (-91-95 x-2 x^2\right )\right ) \, dx=-2 e^x x^2+x^2-91 e^x x \]
[In]
[Out]
Rule 2207
Rule 2225
Rule 2227
Rubi steps \begin{align*} \text {integral}& = x^2+\int e^x \left (-91-95 x-2 x^2\right ) \, dx \\ & = x^2+\int \left (-91 e^x-95 e^x x-2 e^x x^2\right ) \, dx \\ & = x^2-2 \int e^x x^2 \, dx-91 \int e^x \, dx-95 \int e^x x \, dx \\ & = -91 e^x-95 e^x x+x^2-2 e^x x^2+4 \int e^x x \, dx+95 \int e^x \, dx \\ & = 4 e^x-91 e^x x+x^2-2 e^x x^2-4 \int e^x \, dx \\ & = -91 e^x x+x^2-2 e^x x^2 \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \left (2 x+e^x \left (-91-95 x-2 x^2\right )\right ) \, dx=x^2-e^x \left (91 x+2 x^2\right ) \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94
method | result | size |
default | \(-91 \,{\mathrm e}^{x} x -2 \,{\mathrm e}^{x} x^{2}+x^{2}\) | \(17\) |
norman | \(-91 \,{\mathrm e}^{x} x -2 \,{\mathrm e}^{x} x^{2}+x^{2}\) | \(17\) |
risch | \(\left (-2 x^{2}-91 x \right ) {\mathrm e}^{x}+x^{2}\) | \(17\) |
parallelrisch | \(-91 \,{\mathrm e}^{x} x -2 \,{\mathrm e}^{x} x^{2}+x^{2}\) | \(17\) |
parts | \(-91 \,{\mathrm e}^{x} x -2 \,{\mathrm e}^{x} x^{2}+x^{2}\) | \(17\) |
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \left (2 x+e^x \left (-91-95 x-2 x^2\right )\right ) \, dx=x^{2} - {\left (2 \, x^{2} + 91 \, x\right )} e^{x} \]
[In]
[Out]
Time = 0.04 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \left (2 x+e^x \left (-91-95 x-2 x^2\right )\right ) \, dx=x^{2} + \left (- 2 x^{2} - 91 x\right ) e^{x} \]
[In]
[Out]
none
Time = 0.18 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.50 \[ \int \left (2 x+e^x \left (-91-95 x-2 x^2\right )\right ) \, dx=x^{2} - 2 \, {\left (x^{2} - 2 \, x + 2\right )} e^{x} - 95 \, {\left (x - 1\right )} e^{x} - 91 \, e^{x} \]
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \left (2 x+e^x \left (-91-95 x-2 x^2\right )\right ) \, dx=x^{2} - {\left (2 \, x^{2} + 91 \, x\right )} e^{x} \]
[In]
[Out]
Time = 0.05 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.89 \[ \int \left (2 x+e^x \left (-91-95 x-2 x^2\right )\right ) \, dx=x^2-91\,x\,{\mathrm {e}}^x-2\,x^2\,{\mathrm {e}}^x \]
[In]
[Out]