3.1515 \(\int \frac{x^7}{\sqrt{1+x^8}} \, dx\)

Optimal. Leaf size=13 \[ \frac{\sqrt{x^8+1}}{4} \]

[Out]

Sqrt[1 + x^8]/4

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Rubi [A]  time = 0.00831188, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{\sqrt{x^8+1}}{4} \]

Antiderivative was successfully verified.

[In]  Int[x^7/Sqrt[1 + x^8],x]

[Out]

Sqrt[1 + x^8]/4

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Rubi in Sympy [A]  time = 1.66903, size = 8, normalized size = 0.62 \[ \frac{\sqrt{x^{8} + 1}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**7/(x**8+1)**(1/2),x)

[Out]

sqrt(x**8 + 1)/4

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Mathematica [A]  time = 0.00459624, size = 13, normalized size = 1. \[ \frac{\sqrt{x^8+1}}{4} \]

Antiderivative was successfully verified.

[In]  Integrate[x^7/Sqrt[1 + x^8],x]

[Out]

Sqrt[1 + x^8]/4

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Maple [A]  time = 0.005, size = 10, normalized size = 0.8 \[{\frac{1}{4}\sqrt{{x}^{8}+1}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^7/(x^8+1)^(1/2),x)

[Out]

1/4*(x^8+1)^(1/2)

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Maxima [A]  time = 1.41338, size = 12, normalized size = 0.92 \[ \frac{1}{4} \, \sqrt{x^{8} + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^7/sqrt(x^8 + 1),x, algorithm="maxima")

[Out]

1/4*sqrt(x^8 + 1)

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Fricas [A]  time = 0.218609, size = 12, normalized size = 0.92 \[ \frac{1}{4} \, \sqrt{x^{8} + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^7/sqrt(x^8 + 1),x, algorithm="fricas")

[Out]

1/4*sqrt(x^8 + 1)

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Sympy [A]  time = 1.20962, size = 8, normalized size = 0.62 \[ \frac{\sqrt{x^{8} + 1}}{4} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**7/(x**8+1)**(1/2),x)

[Out]

sqrt(x**8 + 1)/4

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GIAC/XCAS [A]  time = 0.227729, size = 12, normalized size = 0.92 \[ \frac{1}{4} \, \sqrt{x^{8} + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^7/sqrt(x^8 + 1),x, algorithm="giac")

[Out]

1/4*sqrt(x^8 + 1)