3.4.22 \(\int \frac {x^5}{(1-a^2 x^2)^3 \tanh ^{-1}(a x)} \, dx\) [322]

Optimal. Leaf size=25 \[ \text {Int}\left (\frac {x^5}{\left (1-a^2 x^2\right )^3 \tanh ^{-1}(a x)},x\right ) \]

[Out]

Unintegrable(x^5/(-a^2*x^2+1)^3/arctanh(a*x),x)

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Rubi [A]
time = 0.05, 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 {x^5}{\left (1-a^2 x^2\right )^3 \tanh ^{-1}(a x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[x^5/((1 - a^2*x^2)^3*ArcTanh[a*x]),x]

[Out]

Defer[Int][x^5/((1 - a^2*x^2)^3*ArcTanh[a*x]), x]

Rubi steps

\begin {align*} \int \frac {x^5}{\left (1-a^2 x^2\right )^3 \tanh ^{-1}(a x)} \, dx &=\int \frac {x^5}{\left (1-a^2 x^2\right )^3 \tanh ^{-1}(a x)} \, dx\\ \end {align*}

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Mathematica [A]
time = 14.59, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^5}{\left (1-a^2 x^2\right )^3 \tanh ^{-1}(a x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[x^5/((1 - a^2*x^2)^3*ArcTanh[a*x]),x]

[Out]

Integrate[x^5/((1 - a^2*x^2)^3*ArcTanh[a*x]), x]

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Maple [A]
time = 5.28, size = 0, normalized size = 0.00 \[\int \frac {x^{5}}{\left (-a^{2} x^{2}+1\right )^{3} \arctanh \left (a x \right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^5/(-a^2*x^2+1)^3/arctanh(a*x),x)

[Out]

int(x^5/(-a^2*x^2+1)^3/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(x^5/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm="maxima")

[Out]

-integrate(x^5/((a^2*x^2 - 1)^3*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(x^5/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm="fricas")

[Out]

integral(-x^5/((a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*arctanh(a*x)), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} - \int \frac {x^{5}}{a^{6} x^{6} \operatorname {atanh}{\left (a x \right )} - 3 a^{4} x^{4} \operatorname {atanh}{\left (a x \right )} + 3 a^{2} x^{2} \operatorname {atanh}{\left (a x \right )} - \operatorname {atanh}{\left (a x \right )}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**5/(-a**2*x**2+1)**3/atanh(a*x),x)

[Out]

-Integral(x**5/(a**6*x**6*atanh(a*x) - 3*a**4*x**4*atanh(a*x) + 3*a**2*x**2*atanh(a*x) - 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(x^5/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm="giac")

[Out]

integrate(-x^5/((a^2*x^2 - 1)^3*arctanh(a*x)), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} -\int \frac {x^5}{\mathrm {atanh}\left (a\,x\right )\,{\left (a^2\,x^2-1\right )}^3} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-x^5/(atanh(a*x)*(a^2*x^2 - 1)^3),x)

[Out]

-int(x^5/(atanh(a*x)*(a^2*x^2 - 1)^3), x)

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