Optimal. Leaf size=10 \[ \frac {1}{4 e^{20} x} \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 30} \begin {gather*} \frac {1}{4 e^{20} x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {\int \frac {1}{x^2} \, dx}{4 e^{20}}\\ &=\frac {1}{4 e^{20} x}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} \frac {1}{4 e^{20} x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.58, size = 7, normalized size = 0.70 \begin {gather*} \frac {e^{\left (-20\right )}}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.18, size = 7, normalized size = 0.70 \begin {gather*} \frac {e^{\left (-20\right )}}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.15, size = 8, normalized size = 0.80
method | result | size |
default | \(\frac {{\mathrm e}^{-20}}{4 x}\) | \(8\) |
risch | \(\frac {{\mathrm e}^{-20}}{4 x}\) | \(8\) |
norman | \(\frac {{\mathrm e}^{-20}}{4 x}\) | \(10\) |
gosper | \(\frac {{\mathrm e}^{x} {\mathrm e}^{-20-x}}{4 x}\) | \(13\) |
meijerg | \(-\frac {\left (-1\right )^{{\mathrm e}^{-20}} x^{{\mathrm e}^{-20}-1} {\mathrm e}^{-20-x} \left (-\frac {{\mathrm e}^{20} x^{-{\mathrm e}^{-20}} \left (-1\right )^{-{\mathrm e}^{-20}} \left (x \,{\mathrm e}^{20}+{\mathrm e}^{20}-1\right ) \Gamma \left (1+{\mathrm e}^{-20}\right ) \Gamma \left (\left ({\mathrm e}^{20}-1\right ) {\mathrm e}^{-20}+1\right ) L_{{\mathrm e}^{-20}}^{\left (\left ({\mathrm e}^{20}-1\right ) {\mathrm e}^{-20}\right )}\relax (x )}{\left ({\mathrm e}^{20}-1\right ) \Gamma \left ({\mathrm e}^{-20}+\left ({\mathrm e}^{20}-1\right ) {\mathrm e}^{-20}+1\right )}+\frac {{\mathrm e}^{40} x^{1-{\mathrm e}^{-20}} \left (-1\right )^{-{\mathrm e}^{-20}} L_{{\mathrm e}^{-20}}^{\left (\left ({\mathrm e}^{20}-1\right ) {\mathrm e}^{-20}+1\right )}\relax (x ) \Gamma \left (1+{\mathrm e}^{-20}\right ) \Gamma \left (\left ({\mathrm e}^{20}-1\right ) {\mathrm e}^{-20}+1\right )}{\left ({\mathrm e}^{20}-1\right ) \Gamma \left ({\mathrm e}^{-20}+\left ({\mathrm e}^{20}-1\right ) {\mathrm e}^{-20}+1\right )}\right )}{4}\) | \(155\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.44, size = 7, normalized size = 0.70 \begin {gather*} \frac {e^{\left (-20\right )}}{4 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.39, size = 7, normalized size = 0.70 \begin {gather*} \frac {{\mathrm {e}}^{-20}}{4\,x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.07, size = 7, normalized size = 0.70 \begin {gather*} \frac {1}{4 x e^{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________