Optimal. Leaf size=27 \[ e^{-\frac{b x}{2}} \sqrt{e^{a+b x}} \text{ExpIntegralEi}\left (\frac{b x}{2}\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.088036, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ e^{-\frac{b x}{2}} \sqrt{e^{a+b x}} \text{ExpIntegralEi}\left (\frac{b x}{2}\right ) \]
Antiderivative was successfully verified.
[In] Int[Sqrt[E^(a + b*x)]/x,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.4813, size = 32, normalized size = 1.19 \[ e^{\frac{a}{2}} e^{- \frac{a}{2} - \frac{b x}{2}} \sqrt{e^{a + b x}} \operatorname{Ei}{\left (\frac{b x}{2} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(exp(b*x+a)**(1/2)/x,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00654141, size = 27, normalized size = 1. \[ e^{-\frac{b x}{2}} \sqrt{e^{a+b x}} \text{ExpIntegralEi}\left (\frac{b x}{2}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[E^(a + b*x)]/x,x]
[Out]
_______________________________________________________________________________________
Maple [B] time = 0.088, size = 57, normalized size = 2.1 \[ \sqrt{{{\rm e}^{bx+a}}}{{\rm e}^{-{\frac{bx}{2}{{\rm e}^{{\frac{a}{2}}}}}}} \left ( \ln \left ( x \right ) -\ln \left ( 2 \right ) +\ln \left ( -b{{\rm e}^{{\frac{a}{2}}}} \right ) -\ln \left ( -{\frac{bx}{2}{{\rm e}^{{\frac{a}{2}}}}} \right ) -{\it Ei} \left ( 1,-{\frac{bx}{2}{{\rm e}^{{\frac{a}{2}}}}} \right ) \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(exp(b*x+a)^(1/2)/x,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.848026, size = 14, normalized size = 0.52 \[{\rm Ei}\left (\frac{1}{2} \, b x\right ) e^{\left (\frac{1}{2} \, a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(1/2*b*x + 1/2*a)/x,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.262248, size = 14, normalized size = 0.52 \[{\rm Ei}\left (\frac{1}{2} \, b x\right ) e^{\left (\frac{1}{2} \, a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(1/2*b*x + 1/2*a)/x,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{e^{a} e^{b x}}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(exp(b*x+a)**(1/2)/x,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.231435, size = 14, normalized size = 0.52 \[{\rm Ei}\left (\frac{1}{2} \, b x\right ) e^{\left (\frac{1}{2} \, a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(e^(1/2*b*x + 1/2*a)/x,x, algorithm="giac")
[Out]