Optimal. Leaf size=20 \[ \frac {1-e^{(16+x)^2}-x^2}{x} \]
________________________________________________________________________________________
Rubi [A] time = 0.08, antiderivative size = 34, normalized size of antiderivative = 1.70, number of steps used = 5, number of rules used = 2, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {14, 2288} \begin {gather*} -\frac {e^{x^2+32 x+256} \left (x^2+16 x\right )}{(x+16) x^2}-x+\frac {1}{x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {e^{256+32 x+x^2} \left (1-32 x-2 x^2\right )}{x^2}+\frac {-1-x^2}{x^2}\right ) \, dx\\ &=\int \frac {e^{256+32 x+x^2} \left (1-32 x-2 x^2\right )}{x^2} \, dx+\int \frac {-1-x^2}{x^2} \, dx\\ &=-\frac {e^{256+32 x+x^2} \left (16 x+x^2\right )}{x^2 (16+x)}+\int \left (-1-\frac {1}{x^2}\right ) \, dx\\ &=\frac {1}{x}-x-\frac {e^{256+32 x+x^2} \left (16 x+x^2\right )}{x^2 (16+x)}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.04, size = 17, normalized size = 0.85 \begin {gather*} -\frac {-1+e^{(16+x)^2}+x^2}{x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.44, size = 19, normalized size = 0.95 \begin {gather*} -\frac {x^{2} + e^{\left (x^{2} + 32 \, x + 256\right )} - 1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.22, size = 19, normalized size = 0.95 \begin {gather*} -\frac {x^{2} + e^{\left (x^{2} + 32 \, x + 256\right )} - 1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 19, normalized size = 0.95
method | result | size |
risch | \(\frac {1}{x}-x -\frac {{\mathrm e}^{\left (x +16\right )^{2}}}{x}\) | \(19\) |
norman | \(\frac {1-x^{2}-{\mathrm e}^{x^{2}+32 x +256}}{x}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} i \, \sqrt {\pi } \operatorname {erf}\left (i \, x + 16 i\right ) - x + \frac {1}{x} - \int \frac {{\left (32 \, x e^{256} - e^{256}\right )} e^{\left (x^{2} + 32 \, x\right )}}{x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.08, size = 20, normalized size = 1.00 \begin {gather*} -x-\frac {{\mathrm {e}}^{x^2+32\,x+256}-1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 15, normalized size = 0.75 \begin {gather*} - x - \frac {e^{x^{2} + 32 x + 256}}{x} + \frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________