Optimal. Leaf size=13 \[ \frac{e^{(a+2) x}}{a+2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0075806, antiderivative size = 13, normalized size of antiderivative = 1., 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 2227
Rule 2194
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 = 0.0033436, size = 13, normalized size = 1. \[ \frac{e^{(a+2) x}}{a+2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.002, size = 15, normalized size = 1.2 \begin{align*}{\frac{{{\rm e}^{ax+2\,x}}}{2+a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.933516, size = 19, normalized size = 1.46 \begin{align*} \frac{e^{\left (a x + 2 \, x\right )}}{a + 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.70432, size = 31, normalized size = 2.38 \begin{align*} \frac{e^{\left ({\left (a + 2\right )} x\right )}}{a + 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.103013, size = 14, normalized size = 1.08 \begin{align*} \begin{cases} \frac{e^{a x + 2 x}}{a + 2} & \text{for}\: a + 2 \neq 0 \\x & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.08114, size = 19, normalized size = 1.46 \begin{align*} \frac{e^{\left (a x + 2 \, x\right )}}{a + 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]