3.193 \(\int \frac {x}{(1-x^2)^{9/8}} \, dx\)

Optimal. Leaf size=13 \[ \frac {4}{\sqrt [8]{1-x^2}} \]

[Out]

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

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {261} \[ \frac {4}{\sqrt [8]{1-x^2}} \]

Antiderivative was successfully verified.

[In]

Int[x/(1 - x^2)^(9/8),x]

[Out]

4/(1 - x^2)^(1/8)

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}{\left (1-x^2\right )^{9/8}} \, dx &=\frac {4}{\sqrt [8]{1-x^2}}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 1.00 \[ \frac {4}{\sqrt [8]{1-x^2}} \]

Antiderivative was successfully verified.

[In]

Integrate[x/(1 - x^2)^(9/8),x]

[Out]

4/(1 - x^2)^(1/8)

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fricas [A]  time = 0.40, size = 18, normalized size = 1.38 \[ -\frac {4 \, {\left (-x^{2} + 1\right )}^{\frac {7}{8}}}{x^{2} - 1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x/(-x^2+1)^(9/8),x, algorithm="fricas")

[Out]

-4*(-x^2 + 1)^(7/8)/(x^2 - 1)

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giac [A]  time = 1.00, size = 11, normalized size = 0.85 \[ \frac {4}{{\left (-x^{2} + 1\right )}^{\frac {1}{8}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x/(-x^2+1)^(9/8),x, algorithm="giac")

[Out]

4/(-x^2 + 1)^(1/8)

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maple [A]  time = 0.00, size = 18, normalized size = 1.38 \[ -\frac {4 \left (x -1\right ) \left (x +1\right )}{\left (-x^{2}+1\right )^{\frac {9}{8}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x/(-x^2+1)^(9/8),x)

[Out]

-4*(x-1)*(x+1)/(-x^2+1)^(9/8)

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maxima [A]  time = 0.41, size = 11, normalized size = 0.85 \[ \frac {4}{{\left (-x^{2} + 1\right )}^{\frac {1}{8}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x/(-x^2+1)^(9/8),x, algorithm="maxima")

[Out]

4/(-x^2 + 1)^(1/8)

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mupad [B]  time = 0.35, size = 11, normalized size = 0.85 \[ \frac {4}{{\left (1-x^2\right )}^{1/8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x/(1 - x^2)^(9/8),x)

[Out]

4/(1 - x^2)^(1/8)

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sympy [A]  time = 0.97, size = 8, normalized size = 0.62 \[ \frac {4}{\sqrt [8]{1 - x^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x/(-x**2+1)**(9/8),x)

[Out]

4/(1 - x**2)**(1/8)

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