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

Optimal. Leaf size=14 \[ \frac{1}{6} x^5 \sqrt{x^2} \]

[Out]

(x^5*Sqrt[x^2])/6

_______________________________________________________________________________________

Rubi [A]  time = 0.00524484, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.286 \[ \frac{1}{6} x^5 \sqrt{x^2} \]

Antiderivative was successfully verified.

[In]  Int[(x^2)^(5/2),x]

[Out]

(x^5*Sqrt[x^2])/6

_______________________________________________________________________________________

Rubi in Sympy [A]  time = 1.09859, size = 10, normalized size = 0.71 \[ \frac{x^{5} \sqrt{x^{2}}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((x**2)**(5/2),x)

[Out]

x**5*sqrt(x**2)/6

_______________________________________________________________________________________

Mathematica [A]  time = 0.00570274, size = 12, normalized size = 0.86 \[ \frac{1}{6} x \left (x^2\right )^{5/2} \]

Antiderivative was successfully verified.

[In]  Integrate[(x^2)^(5/2),x]

[Out]

(x*(x^2)^(5/2))/6

_______________________________________________________________________________________

Maple [A]  time = 0.003, size = 9, normalized size = 0.6 \[{\frac{x}{6} \left ({x}^{2} \right ) ^{{\frac{5}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x^2)^(5/2),x)

[Out]

1/6*x*(x^2)^(5/2)

_______________________________________________________________________________________

Maxima [A]  time = 1.44188, size = 11, normalized size = 0.79 \[ \frac{1}{6} \,{\left (x^{2}\right )}^{\frac{5}{2}} x \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6*(x^2)^(5/2)*x

_______________________________________________________________________________________

Fricas [A]  time = 0.226688, size = 7, normalized size = 0.5 \[ \frac{1}{6} \, x^{6} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6*x^6

_______________________________________________________________________________________

Sympy [A]  time = 0.089224, size = 3, normalized size = 0.21 \[ \frac{x^{6}}{6} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x**2)**(5/2),x)

[Out]

x**6/6

_______________________________________________________________________________________

GIAC/XCAS [A]  time = 0.220911, size = 9, normalized size = 0.64 \[ \frac{1}{6} \, x^{6}{\rm sign}\left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/6*x^6*sign(x)