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

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {x \left (1-a^2 x^2\right )}{\tanh ^{-1}(a x)},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.03, 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 = {} \[ \int \frac {x \left (1-a^2 x^2\right )}{\tanh ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(x*(1 - a^2*x^2))/ArcTanh[a*x],x]

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 0.78, size = 0, normalized size = 0.00 \[ \int \frac {x \left (1-a^2 x^2\right )}{\tanh ^{-1}(a x)} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.60, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {a^{2} x^{3} - x}{\operatorname {artanh}\left (a x\right )}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(-(a^2*x^3 - x)/arctanh(a*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x*(-a^2*x^2+1)/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 = 0.65, size = 0, normalized size = 0.00 \[ \int \frac {x \left (-a^{2} x^{2}+1\right )}{\arctanh \left (a x \right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x*(-a^2*x^2+1)/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 = -0.05 \[ -\int \frac {x\,\left (a^2\,x^2-1\right )}{\mathrm {atanh}\left (a\,x\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(x*(a^2*x^2 - 1))/atanh(a*x),x)

[Out]

-int((x*(a^2*x^2 - 1))/atanh(a*x), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ - \int \left (- \frac {x}{\operatorname {atanh}{\left (a x \right )}}\right )\, dx - \int \frac {a^{2} x^{3}}{\operatorname {atanh}{\left (a x \right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-Integral(-x/atanh(a*x), x) - Integral(a**2*x**3/atanh(a*x), x)

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