Optimal. Leaf size=9 \[ \frac {e^{x^2}}{2} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2240}
\begin {gather*} \frac {e^{x^2}}{2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2240
Rubi steps
\begin {align*} \int e^{x^2} x \, dx &=\frac {e^{x^2}}{2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} \frac {e^{x^2}}{2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.00, size = 7, normalized size = 0.78
method | result | size |
gosper | \(\frac {{\mathrm e}^{x^{2}}}{2}\) | \(7\) |
derivativedivides | \(\frac {{\mathrm e}^{x^{2}}}{2}\) | \(7\) |
default | \(\frac {{\mathrm e}^{x^{2}}}{2}\) | \(7\) |
norman | \(\frac {{\mathrm e}^{x^{2}}}{2}\) | \(7\) |
risch | \(\frac {{\mathrm e}^{x^{2}}}{2}\) | \(7\) |
meijerg | \(-\frac {1}{2}+\frac {{\mathrm e}^{x^{2}}}{2}\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 1.48, size = 6, normalized size = 0.67 \begin {gather*} \frac {1}{2} \, e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 1.37, size = 6, normalized size = 0.67 \begin {gather*} \frac {1}{2} \, e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.02, size = 5, normalized size = 0.56 \begin {gather*} \frac {e^{x^{2}}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.44, size = 6, normalized size = 0.67 \begin {gather*} \frac {1}{2} \, e^{\left (x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.00, size = 6, normalized size = 0.67 \begin {gather*} \frac {{\mathrm {e}}^{x^2}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________