3.97 \(\int \frac{\tan ^{-1}(\coth (a+b x))}{e+f x} \, dx\)

Optimal. Leaf size=17 \[ \text{CannotIntegrate}\left (\frac{\tan ^{-1}(\coth (a+b x))}{e+f x},x\right ) \]

[Out]

CannotIntegrate[ArcTan[Coth[a + b*x]]/(e + f*x), x]

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Rubi [A]  time = 0.0432478, 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 = {} \[ \int \frac{\tan ^{-1}(\coth (a+b x))}{e+f x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[ArcTan[Coth[a + b*x]]/(e + f*x),x]

[Out]

Defer[Int][ArcTan[Coth[a + b*x]]/(e + f*x), x]

Rubi steps

\begin{align*} \int \frac{\tan ^{-1}(\coth (a+b x))}{e+f x} \, dx &=\int \frac{\tan ^{-1}(\coth (a+b x))}{e+f x} \, dx\\ \end{align*}

Mathematica [A]  time = 4.32902, size = 0, normalized size = 0. \[ \int \frac{\tan ^{-1}(\coth (a+b x))}{e+f x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[ArcTan[Coth[a + b*x]]/(e + f*x),x]

[Out]

Integrate[ArcTan[Coth[a + b*x]]/(e + f*x), x]

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Maple [A]  time = 0.872, size = 0, normalized size = 0. \begin{align*} \int{\frac{\arctan \left ({\rm coth} \left (bx+a\right ) \right ) }{fx+e}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(arctan(coth(b*x+a))/(f*x+e),x)

[Out]

int(arctan(coth(b*x+a))/(f*x+e),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\arctan \left (\coth \left (b x + a\right )\right )}{f x + e}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(arctan(coth(b*x+a))/(f*x+e),x, algorithm="maxima")

[Out]

integrate(arctan(coth(b*x + a))/(f*x + e), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\arctan \left (\coth \left (b x + a\right )\right )}{f x + e}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(arctan(coth(b*x+a))/(f*x+e),x, algorithm="fricas")

[Out]

integral(arctan(coth(b*x + a))/(f*x + e), 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(atan(coth(b*x+a))/(f*x+e),x)

[Out]

Timed out

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\arctan \left (\coth \left (b x + a\right )\right )}{f x + e}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(arctan(coth(b*x+a))/(f*x+e),x, algorithm="giac")

[Out]

integrate(arctan(coth(b*x + a))/(f*x + e), x)