Integrand size = 8, antiderivative size = 17 \[ \int -\frac {e^4}{x^3} \, dx=2 \left (\frac {e^4}{4 x^2}-11 \log (3)\right ) \]
[Out]
Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.59, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 30} \[ \int -\frac {e^4}{x^3} \, dx=\frac {e^4}{2 x^2} \]
[In]
[Out]
Rule 12
Rule 30
Rubi steps \begin{align*} \text {integral}& = -\left (e^4 \int \frac {1}{x^3} \, dx\right ) \\ & = \frac {e^4}{2 x^2} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.59 \[ \int -\frac {e^4}{x^3} \, dx=\frac {e^4}{2 x^2} \]
[In]
[Out]
Time = 0.06 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.47
method | result | size |
gosper | \(\frac {{\mathrm e}^{4}}{2 x^{2}}\) | \(8\) |
default | \(\frac {{\mathrm e}^{4}}{2 x^{2}}\) | \(8\) |
norman | \(\frac {{\mathrm e}^{4}}{2 x^{2}}\) | \(8\) |
risch | \(\frac {{\mathrm e}^{4}}{2 x^{2}}\) | \(8\) |
parallelrisch | \(\frac {{\mathrm e}^{4}}{2 x^{2}}\) | \(8\) |
[In]
[Out]
none
Time = 0.25 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.41 \[ \int -\frac {e^4}{x^3} \, dx=\frac {e^{4}}{2 \, x^{2}} \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.41 \[ \int -\frac {e^4}{x^3} \, dx=\frac {e^{4}}{2 x^{2}} \]
[In]
[Out]
none
Time = 0.19 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.41 \[ \int -\frac {e^4}{x^3} \, dx=\frac {e^{4}}{2 \, x^{2}} \]
[In]
[Out]
none
Time = 0.28 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.41 \[ \int -\frac {e^4}{x^3} \, dx=\frac {e^{4}}{2 \, x^{2}} \]
[In]
[Out]
Time = 0.05 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.41 \[ \int -\frac {e^4}{x^3} \, dx=\frac {{\mathrm {e}}^4}{2\,x^2} \]
[In]
[Out]