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

Optimal. Leaf size=23 \[ \text {Int}\left (\frac {1-a^2 x^2}{x \tanh ^{-1}(a x)},x\right ) \]

[Out]

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

Verification is Not applicable to the result.

[In]

Int[(1 - a^2*x^2)/(x*ArcTanh[a*x]),x]

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 1.15, size = 0, normalized size = 0.00 \[ \int \frac {1-a^2 x^2}{x \tanh ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 1.38, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {a^{2} x^{2} - 1}{x \operatorname {artanh}\left (a x\right )}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(-(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 \[ \int -\frac {a^{2} x^{2} - 1}{x \operatorname {artanh}\left (a x\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.64, size = 0, normalized size = 0.00 \[ \int \frac {-a^{2} x^{2}+1}{x \arctanh \left (a x \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(a^2*x^2 - 1)/(x*atanh(a*x)),x)

[Out]

-int((a^2*x^2 - 1)/(x*atanh(a*x)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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