Optimal. Leaf size=32 \[ -\frac{2 a^2}{3 x^{3/2}}-\frac{4 a b}{\sqrt{x}}+2 b^2 \sqrt{x} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0213733, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{2 a^2}{3 x^{3/2}}-\frac{4 a b}{\sqrt{x}}+2 b^2 \sqrt{x} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^2/x^(5/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.93392, size = 31, normalized size = 0.97 \[ - \frac{2 a^{2}}{3 x^{\frac{3}{2}}} - \frac{4 a b}{\sqrt{x}} + 2 b^{2} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**2/x**(5/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0101265, size = 26, normalized size = 0.81 \[ -\frac{2 \left (a^2+6 a b x-3 b^2 x^2\right )}{3 x^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^2/x^(5/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 23, normalized size = 0.7 \[ -{\frac{-6\,{b}^{2}{x}^{2}+12\,abx+2\,{a}^{2}}{3}{x}^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^2/x^(5/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.33665, size = 31, normalized size = 0.97 \[ 2 \, b^{2} \sqrt{x} - \frac{2 \,{\left (6 \, a b x + a^{2}\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2/x^(5/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.207454, size = 32, normalized size = 1. \[ \frac{2 \,{\left (3 \, b^{2} x^{2} - 6 \, a b x - a^{2}\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2/x^(5/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.21081, size = 31, normalized size = 0.97 \[ - \frac{2 a^{2}}{3 x^{\frac{3}{2}}} - \frac{4 a b}{\sqrt{x}} + 2 b^{2} \sqrt{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**2/x**(5/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.210105, size = 31, normalized size = 0.97 \[ 2 \, b^{2} \sqrt{x} - \frac{2 \,{\left (6 \, a b x + a^{2}\right )}}{3 \, x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2/x^(5/2),x, algorithm="giac")
[Out]