3.20 \(\int \frac{\left (b x^2\right )^{3/2}}{x^6} \, dx\)

Optimal. Leaf size=17 \[ -\frac{b \sqrt{b x^2}}{2 x^3} \]

[Out]

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

_______________________________________________________________________________________

Rubi [A]  time = 0.00726617, antiderivative size = 17, 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 \[ -\frac{b \sqrt{b x^2}}{2 x^3} \]

Antiderivative was successfully verified.

[In]  Int[(b*x^2)^(3/2)/x^6,x]

[Out]

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

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 2.0487, size = 15, normalized size = 0.88 \[ - \frac{b \sqrt{b x^{2}}}{2 x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x**2)**(3/2)/x**6,x)

[Out]

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

_______________________________________________________________________________________

Mathematica [A]  time = 0.00254386, size = 16, normalized size = 0.94 \[ -\frac{\left (b x^2\right )^{3/2}}{2 x^5} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x^2)^(3/2)/x^6,x]

[Out]

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

_______________________________________________________________________________________

Maple [A]  time = 0.003, size = 13, normalized size = 0.8 \[ -{\frac{1}{2\,{x}^{5}} \left ( b{x}^{2} \right ) ^{{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x^2)^(3/2)/x^6,x)

[Out]

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

_______________________________________________________________________________________

Maxima [F]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: RuntimeError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2)^(3/2)/x^6,x, algorithm="maxima")

[Out]

Exception raised: RuntimeError

_______________________________________________________________________________________

Fricas [A]  time = 0.233537, size = 18, normalized size = 1.06 \[ -\frac{\sqrt{b x^{2}} b}{2 \, x^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2)^(3/2)/x^6,x, algorithm="fricas")

[Out]

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

_______________________________________________________________________________________

Sympy [A]  time = 3.88315, size = 17, normalized size = 1. \[ - \frac{b^{\frac{3}{2}} \left (x^{2}\right )^{\frac{3}{2}}}{2 x^{5}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x**2)**(3/2)/x**6,x)

[Out]

-b**(3/2)*(x**2)**(3/2)/(2*x**5)

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.218368, size = 14, normalized size = 0.82 \[ -\frac{b^{\frac{3}{2}}{\rm sign}\left (x\right )}{2 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^2)^(3/2)/x^6,x, algorithm="giac")

[Out]

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