3.4.59 \(\int \frac {1}{x^2 (1-a^2 x^2)^4 \tanh ^{-1}(a x)} \, dx\) [359]

Optimal. Leaf size=25 \[ \text {Int}\left (\frac {1}{x^2 \left (1-a^2 x^2\right )^4 \tanh ^{-1}(a x)},x\right ) \]

[Out]

Unintegrable(1/x^2/(-a^2*x^2+1)^4/arctanh(a*x),x)

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Rubi [A]
time = 0.04, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {1}{x^2 \left (1-a^2 x^2\right )^4 \tanh ^{-1}(a x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[1/(x^2*(1 - a^2*x^2)^4*ArcTanh[a*x]),x]

[Out]

Defer[Int][1/(x^2*(1 - a^2*x^2)^4*ArcTanh[a*x]), x]

Rubi steps

\begin {align*} \int \frac {1}{x^2 \left (1-a^2 x^2\right )^4 \tanh ^{-1}(a x)} \, dx &=\int \frac {1}{x^2 \left (1-a^2 x^2\right )^4 \tanh ^{-1}(a x)} \, dx\\ \end {align*}

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Mathematica [A]
time = 2.37, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x^2 \left (1-a^2 x^2\right )^4 \tanh ^{-1}(a x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[1/(x^2*(1 - a^2*x^2)^4*ArcTanh[a*x]),x]

[Out]

Integrate[1/(x^2*(1 - a^2*x^2)^4*ArcTanh[a*x]), x]

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Maple [A]
time = 8.18, size = 0, normalized size = 0.00 \[\int \frac {1}{x^{2} \left (-a^{2} x^{2}+1\right )^{4} \arctanh \left (a x \right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^2/(-a^2*x^2+1)^4/arctanh(a*x),x)

[Out]

int(1/x^2/(-a^2*x^2+1)^4/arctanh(a*x),x)

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm="maxima")

[Out]

integrate(1/((a^2*x^2 - 1)^4*x^2*arctanh(a*x)), x)

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm="fricas")

[Out]

integral(1/((a^8*x^10 - 4*a^6*x^8 + 6*a^4*x^6 - 4*a^2*x^4 + x^2)*arctanh(a*x)), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x^{2} \left (a x - 1\right )^{4} \left (a x + 1\right )^{4} \operatorname {atanh}{\left (a x \right )}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**2/(-a**2*x**2+1)**4/atanh(a*x),x)

[Out]

Integral(1/(x**2*(a*x - 1)**4*(a*x + 1)**4*atanh(a*x)), x)

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm="giac")

[Out]

integrate(1/((a^2*x^2 - 1)^4*x^2*arctanh(a*x)), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {1}{x^2\,\mathrm {atanh}\left (a\,x\right )\,{\left (a^2\,x^2-1\right )}^4} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x^2*atanh(a*x)*(a^2*x^2 - 1)^4),x)

[Out]

int(1/(x^2*atanh(a*x)*(a^2*x^2 - 1)^4), x)

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