Integrand size = 30, antiderivative size = 24 \[ \int \frac {-e^4+e^x (-1+x)-4 x^2+3072 x^4}{4 x^2} \, dx=-2+\frac {e^4+e^x}{4 x}-x+256 x^3 \]
[Out]
Time = 0.03 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.21, number of steps used = 6, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 14, 2228} \[ \int \frac {-e^4+e^x (-1+x)-4 x^2+3072 x^4}{4 x^2} \, dx=256 x^3-x+\frac {e^x}{4 x}+\frac {e^4}{4 x} \]
[In]
[Out]
Rule 12
Rule 14
Rule 2228
Rubi steps \begin{align*} \text {integral}& = \frac {1}{4} \int \frac {-e^4+e^x (-1+x)-4 x^2+3072 x^4}{x^2} \, dx \\ & = \frac {1}{4} \int \left (\frac {e^x (-1+x)}{x^2}+\frac {-e^4-4 x^2+3072 x^4}{x^2}\right ) \, dx \\ & = \frac {1}{4} \int \frac {e^x (-1+x)}{x^2} \, dx+\frac {1}{4} \int \frac {-e^4-4 x^2+3072 x^4}{x^2} \, dx \\ & = \frac {e^x}{4 x}+\frac {1}{4} \int \left (-4-\frac {e^4}{x^2}+3072 x^2\right ) \, dx \\ & = \frac {e^4}{4 x}+\frac {e^x}{4 x}-x+256 x^3 \\ \end{align*}
Time = 0.11 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00 \[ \int \frac {-e^4+e^x (-1+x)-4 x^2+3072 x^4}{4 x^2} \, dx=\frac {e^4+e^x-4 x^2+1024 x^4}{4 x} \]
[In]
[Out]
Time = 0.18 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.88
method | result | size |
parallelrisch | \(\frac {1024 x^{4}-4 x^{2}+{\mathrm e}^{4}+{\mathrm e}^{x}}{4 x}\) | \(21\) |
default | \(-x +256 x^{3}+\frac {{\mathrm e}^{4}}{4 x}+\frac {{\mathrm e}^{x}}{4 x}\) | \(24\) |
norman | \(\frac {-x^{2}+256 x^{4}+\frac {{\mathrm e}^{4}}{4}+\frac {{\mathrm e}^{x}}{4}}{x}\) | \(24\) |
risch | \(-x +256 x^{3}+\frac {{\mathrm e}^{4}}{4 x}+\frac {{\mathrm e}^{x}}{4 x}\) | \(24\) |
parts | \(-x +256 x^{3}+\frac {{\mathrm e}^{4}}{4 x}+\frac {{\mathrm e}^{x}}{4 x}\) | \(24\) |
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int \frac {-e^4+e^x (-1+x)-4 x^2+3072 x^4}{4 x^2} \, dx=\frac {1024 \, x^{4} - 4 \, x^{2} + e^{4} + e^{x}}{4 \, x} \]
[In]
[Out]
Time = 0.07 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.79 \[ \int \frac {-e^4+e^x (-1+x)-4 x^2+3072 x^4}{4 x^2} \, dx=256 x^{3} - x + \frac {e^{x}}{4 x} + \frac {e^{4}}{4 x} \]
[In]
[Out]
Result contains higher order function than in optimal. Order 4 vs. order 3.
Time = 0.22 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.12 \[ \int \frac {-e^4+e^x (-1+x)-4 x^2+3072 x^4}{4 x^2} \, dx=256 \, x^{3} - x + \frac {e^{4}}{4 \, x} + \frac {1}{4} \, {\rm Ei}\left (x\right ) - \frac {1}{4} \, \Gamma \left (-1, -x\right ) \]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int \frac {-e^4+e^x (-1+x)-4 x^2+3072 x^4}{4 x^2} \, dx=\frac {1024 \, x^{4} - 4 \, x^{2} + e^{4} + e^{x}}{4 \, x} \]
[In]
[Out]
Time = 0.08 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {-e^4+e^x (-1+x)-4 x^2+3072 x^4}{4 x^2} \, dx=\frac {\frac {{\mathrm {e}}^4}{4}+\frac {{\mathrm {e}}^x}{4}}{x}-x+256\,x^3 \]
[In]
[Out]