Optimal. Leaf size=16 \[ \frac {2 \sqrt {e^{a+b x}}}{b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2194} \[ \frac {2 \sqrt {e^{a+b x}}}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2194
Rubi steps
\begin {align*} \int \sqrt {e^{a+b x}} \, dx &=\frac {2 \sqrt {e^{a+b x}}}{b}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 16, normalized size = 1.00 \[ \frac {2 \sqrt {e^{a+b x}}}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.42, size = 14, normalized size = 0.88 \[ \frac {2 \, e^{\left (\frac {1}{2} \, b x + \frac {1}{2} \, a\right )}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.32, size = 14, normalized size = 0.88 \[ \frac {2 \, e^{\left (\frac {1}{2} \, b x + \frac {1}{2} \, a\right )}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 14, normalized size = 0.88 \[ \frac {2 \sqrt {{\mathrm e}^{b x +a}}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.87, size = 14, normalized size = 0.88 \[ \frac {2 \, e^{\left (\frac {1}{2} \, b x + \frac {1}{2} \, a\right )}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.39, size = 13, normalized size = 0.81 \[ \frac {2\,\sqrt {{\mathrm {e}}^{a+b\,x}}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.09, size = 14, normalized size = 0.88 \[ \begin {cases} \frac {2 \sqrt {e^{a + b x}}}{b} & \text {for}\: b \neq 0 \\x & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________