3.57 \(\int \frac{x^6}{\left (b x^2\right )^{5/2}} \, dx\)

Optimal. Leaf size=19 \[ \frac{x^3}{2 b^2 \sqrt{b x^2}} \]

[Out]

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

_______________________________________________________________________________________

Rubi [A]  time = 0.00844947, antiderivative size = 19, 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 \[ \frac{x^3}{2 b^2 \sqrt{b x^2}} \]

Antiderivative was successfully verified.

[In]  Int[x^6/(b*x^2)^(5/2),x]

[Out]

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

_______________________________________________________________________________________

Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{\sqrt{b x^{2}} \int x\, dx}{b^{3} x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**6/(b*x**2)**(5/2),x)

[Out]

sqrt(b*x**2)*Integral(x, x)/(b**3*x)

_______________________________________________________________________________________

Mathematica [A]  time = 0.00324527, size = 16, normalized size = 0.84 \[ \frac{x^7}{2 \left (b x^2\right )^{5/2}} \]

Antiderivative was successfully verified.

[In]  Integrate[x^6/(b*x^2)^(5/2),x]

[Out]

x^7/(2*(b*x^2)^(5/2))

_______________________________________________________________________________________

Maple [A]  time = 0.004, size = 13, normalized size = 0.7 \[{\frac{{x}^{7}}{2} \left ( b{x}^{2} \right ) ^{-{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^6/(b*x^2)^(5/2),x)

[Out]

1/2*x^7/(b*x^2)^(5/2)

_______________________________________________________________________________________

Maxima [A]  time = 1.44846, size = 20, normalized size = 1.05 \[ \frac{x^{5}}{2 \, \left (b x^{2}\right )^{\frac{3}{2}} b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^6/(b*x^2)^(5/2),x, algorithm="maxima")

[Out]

1/2*x^5/((b*x^2)^(3/2)*b)

_______________________________________________________________________________________

Fricas [A]  time = 0.251903, size = 18, normalized size = 0.95 \[ \frac{\sqrt{b x^{2}} x}{2 \, b^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^6/(b*x^2)^(5/2),x, algorithm="fricas")

[Out]

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

_______________________________________________________________________________________

Sympy [A]  time = 3.72003, size = 15, normalized size = 0.79 \[ \frac{x^{7}}{2 b^{\frac{5}{2}} \left (x^{2}\right )^{\frac{5}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**6/(b*x**2)**(5/2),x)

[Out]

x**7/(2*b**(5/2)*(x**2)**(5/2))

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.219603, size = 18, normalized size = 0.95 \[ \frac{\sqrt{b x^{2}} x}{2 \, b^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^6/(b*x^2)^(5/2),x, algorithm="giac")

[Out]

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