3.34 \(\int \left (x^2\right )^{7/2} \, dx\)

Optimal. Leaf size=14 \[ \frac{1}{8} x^7 \sqrt{x^2} \]

[Out]

(x^7*Sqrt[x^2])/8

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Rubi [A]  time = 0.00515077, 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 \[ \frac{1}{8} x^7 \sqrt{x^2} \]

Antiderivative was successfully verified.

[In]  Int[(x^2)^(7/2),x]

[Out]

(x^7*Sqrt[x^2])/8

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Rubi in Sympy [A]  time = 1.08604, size = 10, normalized size = 0.71 \[ \frac{x^{7} \sqrt{x^{2}}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((x**2)**(7/2),x)

[Out]

x**7*sqrt(x**2)/8

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Mathematica [A]  time = 0.00591073, size = 12, normalized size = 0.86 \[ \frac{1}{8} x \left (x^2\right )^{7/2} \]

Antiderivative was successfully verified.

[In]  Integrate[(x^2)^(7/2),x]

[Out]

(x*(x^2)^(7/2))/8

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Maple [A]  time = 0.003, size = 9, normalized size = 0.6 \[{\frac{x}{8} \left ({x}^{2} \right ) ^{{\frac{7}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((x^2)^(7/2),x)

[Out]

1/8*x*(x^2)^(7/2)

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Maxima [A]  time = 1.43946, size = 11, normalized size = 0.79 \[ \frac{1}{8} \,{\left (x^{2}\right )}^{\frac{7}{2}} x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2)^(7/2),x, algorithm="maxima")

[Out]

1/8*(x^2)^(7/2)*x

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Fricas [A]  time = 0.217439, size = 7, normalized size = 0.5 \[ \frac{1}{8} \, x^{8} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2)^(7/2),x, algorithm="fricas")

[Out]

1/8*x^8

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Sympy [A]  time = 0.105236, size = 3, normalized size = 0.21 \[ \frac{x^{8}}{8} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x**2)**(7/2),x)

[Out]

x**8/8

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GIAC/XCAS [A]  time = 0.220829, size = 9, normalized size = 0.64 \[ \frac{1}{8} \, x^{8}{\rm sign}\left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((x^2)^(7/2),x, algorithm="giac")

[Out]

1/8*x^8*sign(x)