3.94 \(\int (d x)^m (a+b \tanh ^{-1}(c x^2))^3 \, dx\)

Optimal. Leaf size=20 \[ \text{Unintegrable}\left ((d x)^m \left (a+b \tanh ^{-1}\left (c x^2\right )\right )^3,x\right ) \]

[Out]

Unintegrable[(d*x)^m*(a + b*ArcTanh[c*x^2])^3, x]

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Rubi [A]  time = 0.0239834, 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 = {} \[ \int (d x)^m \left (a+b \tanh ^{-1}\left (c x^2\right )\right )^3 \, dx \]

Verification is Not applicable to the result.

[In]

Int[(d*x)^m*(a + b*ArcTanh[c*x^2])^3,x]

[Out]

Defer[Int][(d*x)^m*(a + b*ArcTanh[c*x^2])^3, x]

Rubi steps

\begin{align*} \int (d x)^m \left (a+b \tanh ^{-1}\left (c x^2\right )\right )^3 \, dx &=\int (d x)^m \left (a+b \tanh ^{-1}\left (c x^2\right )\right )^3 \, dx\\ \end{align*}

Mathematica [A]  time = 1.75129, size = 0, normalized size = 0. \[ \int (d x)^m \left (a+b \tanh ^{-1}\left (c x^2\right )\right )^3 \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(d*x)^m*(a + b*ArcTanh[c*x^2])^3,x]

[Out]

Integrate[(d*x)^m*(a + b*ArcTanh[c*x^2])^3, x]

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Maple [A]  time = 0.122, size = 0, normalized size = 0. \begin{align*} \int \left ( dx \right ) ^{m} \left ( a+b{\it Artanh} \left ( c{x}^{2} \right ) \right ) ^{3}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*x)^m*(a+b*arctanh(c*x^2))^3,x)

[Out]

int((d*x)^m*(a+b*arctanh(c*x^2))^3,x)

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Maxima [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x)^m*(a+b*arctanh(c*x^2))^3,x, algorithm="maxima")

[Out]

Exception raised: ValueError

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left ({\left (b^{3} \operatorname{artanh}\left (c x^{2}\right )^{3} + 3 \, a b^{2} \operatorname{artanh}\left (c x^{2}\right )^{2} + 3 \, a^{2} b \operatorname{artanh}\left (c x^{2}\right ) + a^{3}\right )} \left (d x\right )^{m}, 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))^3,x, algorithm="fricas")

[Out]

integral((b^3*arctanh(c*x^2)^3 + 3*a*b^2*arctanh(c*x^2)^2 + 3*a^2*b*arctanh(c*x^2) + a^3)*(d*x)^m, 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))**3,x)

[Out]

Timed out

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (b \operatorname{artanh}\left (c x^{2}\right ) + a\right )}^{3} \left (d x\right )^{m}\,{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))^3,x, algorithm="giac")

[Out]

integrate((b*arctanh(c*x^2) + a)^3*(d*x)^m, x)