Integrand size = 30, antiderivative size = 23 \[ \int \frac {e^{3/x} (-3+x)-x-e^4 x-8 x^2}{x} \, dx=2-x+\left (-e^4+e^{3/x}-4 x\right ) x \]
[Out]
Time = 0.03 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {6, 14, 2326} \[ \int \frac {e^{3/x} (-3+x)-x-e^4 x-8 x^2}{x} \, dx=-4 x^2+e^{3/x} x-\left (1+e^4\right ) x \]
[In]
[Out]
Rule 6
Rule 14
Rule 2326
Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{3/x} (-3+x)+\left (-1-e^4\right ) x-8 x^2}{x} \, dx \\ & = \int \left (-1-e^4+\frac {e^{3/x} (-3+x)}{x}-8 x\right ) \, dx \\ & = -\left (\left (1+e^4\right ) x\right )-4 x^2+\int \frac {e^{3/x} (-3+x)}{x} \, dx \\ & = e^{3/x} x-\left (1+e^4\right ) x-4 x^2 \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04 \[ \int \frac {e^{3/x} (-3+x)-x-e^4 x-8 x^2}{x} \, dx=-x-e^4 x+e^{3/x} x-4 x^2 \]
[In]
[Out]
Time = 0.46 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00
method | result | size |
derivativedivides | \(-4 x^{2}-x -x \,{\mathrm e}^{4}+x \,{\mathrm e}^{\frac {3}{x}}\) | \(23\) |
default | \(-4 x^{2}-x -x \,{\mathrm e}^{4}+x \,{\mathrm e}^{\frac {3}{x}}\) | \(23\) |
norman | \(x \,{\mathrm e}^{\frac {3}{x}}+\left (-{\mathrm e}^{4}-1\right ) x -4 x^{2}\) | \(23\) |
risch | \(-4 x^{2}-x -x \,{\mathrm e}^{4}+x \,{\mathrm e}^{\frac {3}{x}}\) | \(23\) |
parallelrisch | \(-4 x^{2}-x -x \,{\mathrm e}^{4}+x \,{\mathrm e}^{\frac {3}{x}}\) | \(23\) |
parts | \(-4 x^{2}-x -x \,{\mathrm e}^{4}+x \,{\mathrm e}^{\frac {3}{x}}\) | \(23\) |
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.96 \[ \int \frac {e^{3/x} (-3+x)-x-e^4 x-8 x^2}{x} \, dx=-4 \, x^{2} - x e^{4} + x e^{\frac {3}{x}} - x \]
[In]
[Out]
Time = 0.07 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.83 \[ \int \frac {e^{3/x} (-3+x)-x-e^4 x-8 x^2}{x} \, dx=- 4 x^{2} + x e^{\frac {3}{x}} + x \left (- e^{4} - 1\right ) \]
[In]
[Out]
Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.22 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.35 \[ \int \frac {e^{3/x} (-3+x)-x-e^4 x-8 x^2}{x} \, dx=-4 \, x^{2} - x e^{4} - x + 3 \, {\rm Ei}\left (\frac {3}{x}\right ) - 3 \, \Gamma \left (-1, -\frac {3}{x}\right ) \]
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.17 \[ \int \frac {e^{3/x} (-3+x)-x-e^4 x-8 x^2}{x} \, dx=-x^{2} {\left (\frac {e^{4}}{x} - \frac {e^{\frac {3}{x}}}{x} + \frac {1}{x} + 4\right )} \]
[In]
[Out]
Time = 12.83 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.78 \[ \int \frac {e^{3/x} (-3+x)-x-e^4 x-8 x^2}{x} \, dx=-x\,\left (4\,x+{\mathrm {e}}^4-{\mathrm {e}}^{3/x}+1\right ) \]
[In]
[Out]