3.185 \(\int \frac{(d x)^m}{a+b \tanh ^{-1}(\frac{c}{x^2})} \, dx\)

Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{(d x)^m}{a+b \tanh ^{-1}\left (\frac{c}{x^2}\right )},x\right ) \]

[Out]

Unintegrable[(d*x)^m/(a + b*ArcTanh[c/x^2]), x]

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Rubi [A]  time = 0.027983, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{(d x)^m}{a+b \tanh ^{-1}\left (\frac{c}{x^2}\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(d*x)^m/(a + b*ArcTanh[c/x^2]),x]

[Out]

Defer[Int][(d*x)^m/(a + b*ArcTanh[c/x^2]), x]

Rubi steps

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

Mathematica [A]  time = 0.402949, size = 0, normalized size = 0. \[ \int \frac{(d x)^m}{a+b \tanh ^{-1}\left (\frac{c}{x^2}\right )} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(d*x)^m/(a + b*ArcTanh[c/x^2]),x]

[Out]

Integrate[(d*x)^m/(a + b*ArcTanh[c/x^2]), x]

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Maple [A]  time = 0.185, size = 0, normalized size = 0. \begin{align*} \int{ \left ( dx \right ) ^{m} \left ( a+b{\it Artanh} \left ({\frac{c}{{x}^{2}}} \right ) \right ) ^{-1}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*x)^m/(a+b*arctanh(c/x^2)),x)

[Out]

int((d*x)^m/(a+b*arctanh(c/x^2)),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (d x\right )^{m}}{b \operatorname{artanh}\left (\frac{c}{x^{2}}\right ) + a}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x)^m/(a+b*arctanh(c/x^2)),x, algorithm="maxima")

[Out]

integrate((d*x)^m/(b*arctanh(c/x^2) + a), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\left (d x\right )^{m}}{b \operatorname{artanh}\left (\frac{c}{x^{2}}\right ) + a}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x)^m/(a+b*arctanh(c/x^2)),x, algorithm="fricas")

[Out]

integral((d*x)^m/(b*arctanh(c/x^2) + a), x)

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x)**m/(a+b*atanh(c/x**2)),x)

[Out]

Timed out

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (d x\right )^{m}}{b \operatorname{artanh}\left (\frac{c}{x^{2}}\right ) + a}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x)^m/(a+b*arctanh(c/x^2)),x, algorithm="giac")

[Out]

integrate((d*x)^m/(b*arctanh(c/x^2) + a), x)