3.39 \(\int \frac{x^2}{\sqrt{b x^2}} \, dx\)

Optimal. Leaf size=16 \[ \frac{x^3}{2 \sqrt{b x^2}} \]

[Out]

x^3/(2*Sqrt[b*x^2])

_______________________________________________________________________________________

Rubi [A]  time = 0.00664445, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{x^3}{2 \sqrt{b x^2}} \]

Antiderivative was successfully verified.

[In]  Int[x^2/Sqrt[b*x^2],x]

[Out]

x^3/(2*Sqrt[b*x^2])

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{\sqrt{b x^{2}} \int x\, dx}{b x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**2/(b*x**2)**(1/2),x)

[Out]

sqrt(b*x**2)*Integral(x, x)/(b*x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00253715, size = 16, normalized size = 1. \[ \frac{x^3}{2 \sqrt{b x^2}} \]

Antiderivative was successfully verified.

[In]  Integrate[x^2/Sqrt[b*x^2],x]

[Out]

x^3/(2*Sqrt[b*x^2])

_______________________________________________________________________________________

Maple [A]  time = 0.002, size = 13, normalized size = 0.8 \[{\frac{{x}^{3}}{2}{\frac{1}{\sqrt{b{x}^{2}}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^2/(b*x^2)^(1/2),x)

[Out]

1/2*x^3/(b*x^2)^(1/2)

_______________________________________________________________________________________

Maxima [A]  time = 1.4336, size = 11, normalized size = 0.69 \[ \frac{x^{2}}{2 \, \sqrt{b}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2/sqrt(b*x^2),x, algorithm="maxima")

[Out]

1/2*x^2/sqrt(b)

_______________________________________________________________________________________

Fricas [A]  time = 0.214799, size = 18, normalized size = 1.12 \[ \frac{\sqrt{b x^{2}} x}{2 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2/sqrt(b*x^2),x, algorithm="fricas")

[Out]

1/2*sqrt(b*x^2)*x/b

_______________________________________________________________________________________

Sympy [A]  time = 1.66752, size = 15, normalized size = 0.94 \[ \frac{x^{3}}{2 \sqrt{b} \sqrt{x^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**2/(b*x**2)**(1/2),x)

[Out]

x**3/(2*sqrt(b)*sqrt(x**2))

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.220003, size = 18, normalized size = 1.12 \[ \frac{\sqrt{b x^{2}} x}{2 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^2/sqrt(b*x^2),x, algorithm="giac")

[Out]

1/2*sqrt(b*x^2)*x/b