Optimal. Leaf size=17 \[ 2 b \sqrt{x}-\frac{2 a}{\sqrt{x}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.012567, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ 2 b \sqrt{x}-\frac{2 a}{\sqrt{x}} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)/x^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.31643, size = 15, normalized size = 0.88 \[ - \frac{2 a}{\sqrt{x}} + 2 b \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)/x**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00537955, size = 14, normalized size = 0.82 \[ \frac{2 (b x-a)}{\sqrt{x}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)/x^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.004, size = 12, normalized size = 0.7 \[ -2\,{\frac{-bx+a}{\sqrt{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)/x^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.3457, size = 18, normalized size = 1.06 \[ 2 \, b \sqrt{x} - \frac{2 \, a}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/x^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.210057, size = 16, normalized size = 0.94 \[ \frac{2 \,{\left (b x - a\right )}}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/x^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.31541, size = 15, normalized size = 0.88 \[ - \frac{2 a}{\sqrt{x}} + 2 b \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)/x**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.202568, size = 18, normalized size = 1.06 \[ 2 \, b \sqrt{x} - \frac{2 \, a}{\sqrt{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)/x^(3/2),x, algorithm="giac")
[Out]