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

Optimal. Leaf size=22 \[ \text {Int}\left (\frac {\tanh ^{-1}(d (-\tanh (a+b x))-d+1)}{x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.07, 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 = {} \[ \int \frac {\tanh ^{-1}(1-d-d \tanh (a+b x))}{x} \, dx \]

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*}

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Mathematica [A]  time = 5.89, size = 0, normalized size = 0.00 \[ \int \frac {\tanh ^{-1}(1-d-d \tanh (a+b x))}{x} \, dx \]

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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fricas [A]  time = 0.45, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {\operatorname {artanh}\left (d \tanh \left (b x + a\right ) + d - 1\right )}{x}, x\right ) \]

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

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)

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maple [A]  time = 0.94, size = 0, normalized size = 0.00 \[ \int -\frac {\arctanh \left (-1+d +d \tanh \left (b x +a \right )\right )}{x}\, dx \]

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 = 0.00, size = 0, normalized size = 0.00 \[ -\int \frac {\operatorname {artanh}\left (d \tanh \left (b x + a\right ) + d - 1\right )}{x}\,{d x} \]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

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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