3.2.86 \(\int \frac {1-a^2 x^2}{\tanh ^{-1}(a x)} \, dx\) [186]

Optimal. Leaf size=20 \[ \text {Int}\left (\frac {1-a^2 x^2}{\tanh ^{-1}(a x)},x\right ) \]

[Out]

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

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Rubi [A]
time = 0.01, 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-a^2 x^2}{\tanh ^{-1}(a x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(1 - a^2*x^2)/ArcTanh[a*x],x]

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 0.23, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1-a^2 x^2}{\tanh ^{-1}(a x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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Maple [A]
time = 32.66, size = 0, normalized size = 0.00 \[\int \frac {-a^{2} x^{2}+1}{\arctanh \left (a x \right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

[Out]

integral(-(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 {a^{2} x^{2}}{\operatorname {atanh}{\left (a x \right )}}\, dx - \int \left (- \frac {1}{\operatorname {atanh}{\left (a x \right )}}\right )\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} -\int \frac {a^2\,x^2-1}{\mathrm {atanh}\left (a\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(a^2*x^2 - 1)/atanh(a*x),x)

[Out]

-int((a^2*x^2 - 1)/atanh(a*x), x)

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