3.14 \(\int \frac {x^5}{\sqrt {1-x^6}} \, dx\)

Optimal. Leaf size=15 \[ -\frac {1}{3} \sqrt {1-x^6} \]

[Out]

-1/3*(-x^6+1)^(1/2)

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Rubi [A]  time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {261} \[ -\frac {1}{3} \sqrt {1-x^6} \]

Antiderivative was successfully verified.

[In]

Int[x^5/Sqrt[1 - x^6],x]

[Out]

-Sqrt[1 - x^6]/3

Rule 261

Int[(x_)^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[(a + b*x^n)^(p + 1)/(b*n*(p + 1)), x] /; FreeQ
[{a, b, m, n, p}, x] && EqQ[m, n - 1] && NeQ[p, -1]

Rubi steps

\begin {align*} \int \frac {x^5}{\sqrt {1-x^6}} \, dx &=-\frac {1}{3} \sqrt {1-x^6}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 1.00 \[ -\frac {1}{3} \sqrt {1-x^6} \]

Antiderivative was successfully verified.

[In]

Integrate[x^5/Sqrt[1 - x^6],x]

[Out]

-1/3*Sqrt[1 - x^6]

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fricas [A]  time = 0.40, size = 11, normalized size = 0.73 \[ -\frac {1}{3} \, \sqrt {-x^{6} + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^5/(-x^6+1)^(1/2),x, algorithm="fricas")

[Out]

-1/3*sqrt(-x^6 + 1)

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giac [A]  time = 0.01, size = 11, normalized size = 0.73 \[ -\frac {1}{3} \, \sqrt {-x^{6} + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^5/(-x^6+1)^(1/2),x, algorithm="giac")

[Out]

-1/3*sqrt(-x^6 + 1)

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maple [B]  time = 0.01, size = 32, normalized size = 2.13 \[ \frac {\left (x -1\right ) \left (x +1\right ) \left (x^{2}+x +1\right ) \left (x^{2}-x +1\right )}{3 \sqrt {-x^{6}+1}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^5/(-x^6+1)^(1/2),x)

[Out]

1/3*(-1+x)*(x+1)*(x^2+x+1)*(x^2-x+1)/(-x^6+1)^(1/2)

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maxima [A]  time = 0.46, size = 11, normalized size = 0.73 \[ -\frac {1}{3} \, \sqrt {-x^{6} + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^5/(-x^6+1)^(1/2),x, algorithm="maxima")

[Out]

-1/3*sqrt(-x^6 + 1)

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mupad [B]  time = 0.35, size = 11, normalized size = 0.73 \[ -\frac {\sqrt {1-x^6}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^5/(1 - x^6)^(1/2),x)

[Out]

-(1 - x^6)^(1/2)/3

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sympy [A]  time = 0.27, size = 10, normalized size = 0.67 \[ - \frac {\sqrt {1 - x^{6}}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**5/(-x**6+1)**(1/2),x)

[Out]

-sqrt(1 - x**6)/3

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