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

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)

________________________________________________________________________________________

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

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*}

________________________________________________________________________________________

Mathematica [A]  time = 0.34, size = 0, normalized size = 0.00 \[ \int \frac {1-a^2 x^2}{\tanh ^{-1}(a x)} \, dx \]

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]

________________________________________________________________________________________

fricas [A]  time = 0.70, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {a^{2} x^{2} - 1}{\operatorname {artanh}\left (a x\right )}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

maple [A]  time = 0.62, 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)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(a^2*x^2 - 1)/atanh(a*x),x)

[Out]

-int((a^2*x^2 - 1)/atanh(a*x), x)

________________________________________________________________________________________

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

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)

________________________________________________________________________________________