Optimal. Leaf size=23 \[ 25-\frac {e^x \left (-256 (1-x)^2-x\right )}{x} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.07, antiderivative size = 20, normalized size of antiderivative = 0.87, number of steps
used = 8, number of rules used = 5, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.227, Rules used = {2230, 2225,
2208, 2209, 2207} \begin {gather*} 256 e^x x-511 e^x+\frac {256 e^x}{x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2207
Rule 2208
Rule 2209
Rule 2225
Rule 2230
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-255 e^x-\frac {256 e^x}{x^2}+\frac {256 e^x}{x}+256 e^x x\right ) \, dx\\ &=-\left (255 \int e^x \, dx\right )-256 \int \frac {e^x}{x^2} \, dx+256 \int \frac {e^x}{x} \, dx+256 \int e^x x \, dx\\ &=-255 e^x+\frac {256 e^x}{x}+256 e^x x+256 \text {Ei}(x)-256 \int e^x \, dx-256 \int \frac {e^x}{x} \, dx\\ &=-511 e^x+\frac {256 e^x}{x}+256 e^x x\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.06, size = 14, normalized size = 0.61 \begin {gather*} e^x \left (-511+\frac {256}{x}+256 x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.68, size = 18, normalized size = 0.78
method | result | size |
gosper | \(\frac {\left (256 x^{2}-511 x +256\right ) {\mathrm e}^{x}}{x}\) | \(17\) |
risch | \(\frac {\left (256 x^{2}-511 x +256\right ) {\mathrm e}^{x}}{x}\) | \(17\) |
default | \(\frac {256 \,{\mathrm e}^{x}}{x}+256 \,{\mathrm e}^{x} x -511 \,{\mathrm e}^{x}\) | \(18\) |
norman | \(\frac {-511 \,{\mathrm e}^{x} x +256 \,{\mathrm e}^{x} x^{2}+256 \,{\mathrm e}^{x}}{x}\) | \(22\) |
meijerg | \(767-128 \left (-2 x +2\right ) {\mathrm e}^{x}-255 \,{\mathrm e}^{x}-\frac {128 \left (2 x +2\right )}{x}+\frac {256 \,{\mathrm e}^{x}}{x}+\frac {256}{x}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.29, size = 23, normalized size = 1.00 \begin {gather*} 256 \, {\left (x - 1\right )} e^{x} + 256 \, {\rm Ei}\left (x\right ) - 255 \, e^{x} - 256 \, \Gamma \left (-1, -x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 16, normalized size = 0.70 \begin {gather*} \frac {{\left (256 \, x^{2} - 511 \, x + 256\right )} e^{x}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.03, size = 14, normalized size = 0.61 \begin {gather*} \frac {\left (256 x^{2} - 511 x + 256\right ) e^{x}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.43, size = 21, normalized size = 0.91 \begin {gather*} \frac {256 \, x^{2} e^{x} - 511 \, x e^{x} + 256 \, e^{x}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.07, size = 16, normalized size = 0.70 \begin {gather*} \frac {{\mathrm {e}}^x\,\left (256\,x^2-511\,x+256\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________