Optimal. Leaf size=16 \[ \frac{2 \sqrt{e^{a+b x}}}{b} \]
[Out]
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Rubi [A] time = 0.0125971, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{2 \sqrt{e^{a+b x}}}{b} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[E^(a + b*x)],x]
[Out]
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Rubi in Sympy [A] time = 1.19301, size = 12, normalized size = 0.75 \[ \frac{2 \sqrt{e^{a + b x}}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(b*x+a)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00296304, size = 16, normalized size = 1. \[ \frac{2 \sqrt{e^{a+b x}}}{b} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[E^(a + b*x)],x]
[Out]
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Maple [A] time = 0.003, size = 14, normalized size = 0.9 \[ 2\,{\frac{\sqrt{{{\rm e}^{bx+a}}}}{b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(b*x+a)^(1/2),x)
[Out]
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Maxima [A] time = 0.787282, size = 19, normalized size = 1.19 \[ \frac{2 \, e^{\left (\frac{1}{2} \, b x + \frac{1}{2} \, a\right )}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(1/2*b*x + 1/2*a),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.248416, size = 19, normalized size = 1.19 \[ \frac{2 \, e^{\left (\frac{1}{2} \, b x + \frac{1}{2} \, a\right )}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(1/2*b*x + 1/2*a),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.1371, 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] integrate(exp(b*x+a)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.237854, size = 19, normalized size = 1.19 \[ \frac{2 \, e^{\left (\frac{1}{2} \, b x + \frac{1}{2} \, a\right )}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(1/2*b*x + 1/2*a),x, algorithm="giac")
[Out]