3.220 \(\int \frac {(1-a^2 x^2)^2}{x \tanh ^{-1}(a x)} \, dx\)

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

[Out]

Unintegrable((-a^2*x^2+1)^2/x/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 = {} \[ \int \frac {\left (1-a^2 x^2\right )^2}{x \tanh ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 1.46, size = 0, normalized size = 0.00 \[ \int \frac {\left (1-a^2 x^2\right )^2}{x \tanh ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.64, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}{x \operatorname {artanh}\left (a x\right )}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (a^{2} x^{2} - 1\right )}^{2}}{x \operatorname {artanh}\left (a x\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.95, size = 0, normalized size = 0.00 \[ \int \frac {\left (-a^{2} x^{2}+1\right )^{2}}{x \arctanh \left (a x \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (a^{2} x^{2} - 1\right )}^{2}}{x \operatorname {artanh}\left (a x\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a^2*x^2 - 1)^2/(x*atanh(a*x)),x)

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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