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

Optimal. Leaf size=19 \[ \frac{1}{7} b^2 x^6 \sqrt{b x^2} \]

[Out]

(b^2*x^6*Sqrt[b*x^2])/7

_______________________________________________________________________________________

Rubi [A]  time = 0.00849907, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ \frac{1}{7} b^2 x^6 \sqrt{b x^2} \]

Antiderivative was successfully verified.

[In]  Int[x*(b*x^2)^(5/2),x]

[Out]

(b^2*x^6*Sqrt[b*x^2])/7

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 2.14828, size = 10, normalized size = 0.53 \[ \frac{\left (b x^{2}\right )^{\frac{7}{2}}}{7 b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

_______________________________________________________________________________________

Mathematica [A]  time = 0.00304912, size = 16, normalized size = 0.84 \[ \frac{1}{7} x^2 \left (b x^2\right )^{5/2} \]

Antiderivative was successfully verified.

[In]  Integrate[x*(b*x^2)^(5/2),x]

[Out]

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

_______________________________________________________________________________________

Maple [A]  time = 0.005, size = 13, normalized size = 0.7 \[{\frac{{x}^{2}}{7} \left ( b{x}^{2} \right ) ^{{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x*(b*x^2)^(5/2),x)

[Out]

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

_______________________________________________________________________________________

Maxima [A]  time = 1.43312, size = 16, normalized size = 0.84 \[ \frac{\left (b x^{2}\right )^{\frac{7}{2}}}{7 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

_______________________________________________________________________________________

Fricas [A]  time = 0.219742, size = 20, normalized size = 1.05 \[ \frac{1}{7} \, \sqrt{b x^{2}} b^{2} x^{6} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/7*sqrt(b*x^2)*b^2*x^6

_______________________________________________________________________________________

Sympy [A]  time = 4.93474, size = 15, normalized size = 0.79 \[ \frac{b^{\frac{5}{2}} x^{2} \left (x^{2}\right )^{\frac{5}{2}}}{7} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x*(b*x**2)**(5/2),x)

[Out]

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

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.227917, size = 14, normalized size = 0.74 \[ \frac{1}{7} \, b^{\frac{5}{2}} x^{7}{\rm sign}\left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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