Optimal. Leaf size=13 \[ \frac {e^{(a+2) x}}{a+2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {2227, 2194} \[ \frac {e^{(a+2) x}}{a+2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2194
Rule 2227
Rubi steps
\begin {align*} \int e^{2 x+a x} \, dx &=\int e^{(2+a) x} \, dx\\ &=\frac {e^{(2+a) x}}{2+a}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \[ \frac {e^{(a+2) x}}{a+2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.40, size = 12, normalized size = 0.92 \[ \frac {e^{\left ({\left (a + 2\right )} x\right )}}{a + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.12, size = 14, normalized size = 1.08 \[ \frac {e^{\left (a x + 2 \, x\right )}}{a + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 15, normalized size = 1.15 \[ \frac {{\mathrm e}^{a x +2 x}}{a +2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.42, size = 14, normalized size = 1.08 \[ \frac {e^{\left (a x + 2 \, x\right )}}{a + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 14, normalized size = 1.08 \[ \frac {{\mathrm {e}}^{2\,x+a\,x}}{a+2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.09, size = 14, normalized size = 1.08 \[ \begin {cases} \frac {e^{a x + 2 x}}{a + 2} & \text {for}\: a + 2 \neq 0 \\x & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________