3.297 \(\int \frac{\tanh ^{-1}(1-d-d \tanh (a+b x))}{x} \, dx\)

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

[Out]

CannotIntegrate[ArcTanh[1 - d - d*Tanh[a + b*x]]/x, x]

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Rubi [A]  time = 0.0667474, 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 = {} \[ \int \frac{\tanh ^{-1}(1-d-d \tanh (a+b x))}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[ArcTanh[1 - d - d*Tanh[a + b*x]]/x,x]

[Out]

Defer[Int][ArcTanh[1 - d - d*Tanh[a + b*x]]/x, x]

Rubi steps

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

Mathematica [A]  time = 5.20367, size = 0, normalized size = 0. \[ \int \frac{\tanh ^{-1}(1-d-d \tanh (a+b x))}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[ArcTanh[1 - d - d*Tanh[a + b*x]]/x,x]

[Out]

Integrate[ArcTanh[1 - d - d*Tanh[a + b*x]]/x, x]

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Maple [A]  time = 0.329, size = 0, normalized size = 0. \begin{align*} \int -{\frac{{\it Artanh} \left ( -1+d+d\tanh \left ( bx+a \right ) \right ) }{x}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-arctanh(-1+d+d*tanh(b*x+a))/x,x)

[Out]

int(-arctanh(-1+d+d*tanh(b*x+a))/x,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} -\int \frac{\operatorname{artanh}\left (d \tanh \left (b x + a\right ) + d - 1\right )}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-arctanh(-1+d+d*tanh(b*x+a))/x,x, algorithm="maxima")

[Out]

-integrate(arctanh(d*tanh(b*x + a) + d - 1)/x, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (-\frac{\operatorname{artanh}\left (d \tanh \left (b x + a\right ) + d - 1\right )}{x}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-arctanh(-1+d+d*tanh(b*x+a))/x,x, algorithm="fricas")

[Out]

integral(-arctanh(d*tanh(b*x + a) + d - 1)/x, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} - \int \frac{\operatorname{atanh}{\left (d \tanh{\left (a + b x \right )} + d - 1 \right )}}{x}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-atanh(-1+d+d*tanh(b*x+a))/x,x)

[Out]

-Integral(atanh(d*tanh(a + b*x) + d - 1)/x, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int -\frac{\operatorname{artanh}\left (d \tanh \left (b x + a\right ) + d - 1\right )}{x}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-arctanh(-1+d+d*tanh(b*x+a))/x,x, algorithm="giac")

[Out]

integrate(-arctanh(d*tanh(b*x + a) + d - 1)/x, x)