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

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

[Out]

CannotIntegrate[ArcCoth[Tan[a + b*x]]/(e + f*x), x]

________________________________________________________________________________________

Rubi [A]  time = 0.0410895, 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 = {} \[ \int \frac{\coth ^{-1}(\tan (a+b x))}{e+f x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[ArcCoth[Tan[a + b*x]]/(e + f*x),x]

[Out]

Defer[Int][ArcCoth[Tan[a + b*x]]/(e + f*x), x]

Rubi steps

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

Mathematica [A]  time = 5.06394, size = 0, normalized size = 0. \[ \int \frac{\coth ^{-1}(\tan (a+b x))}{e+f x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[ArcCoth[Tan[a + b*x]]/(e + f*x),x]

[Out]

Integrate[ArcCoth[Tan[a + b*x]]/(e + f*x), x]

________________________________________________________________________________________

Maple [A]  time = 1.157, size = 0, normalized size = 0. \begin{align*} \int{\frac{{\rm arccoth} \left (\tan \left ( bx+a \right ) \right )}{fx+e}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(arccoth(tan(b*x+a))/(f*x+e),x)

[Out]

int(arccoth(tan(b*x+a))/(f*x+e),x)

________________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{arcoth}\left (\tan \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(arccoth(tan(b*x+a))/(f*x+e),x, algorithm="maxima")

[Out]

integrate(arccoth(tan(b*x + a))/(f*x + e), x)

________________________________________________________________________________________

Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\operatorname{arcoth}\left (\tan \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(arccoth(tan(b*x+a))/(f*x+e),x, algorithm="fricas")

[Out]

integral(arccoth(tan(b*x + a))/(f*x + e), x)

________________________________________________________________________________________

Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{acoth}{\left (\tan{\left (a + b x \right )} \right )}}{e + f x}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(acoth(tan(b*x+a))/(f*x+e),x)

[Out]

Integral(acoth(tan(a + b*x))/(e + f*x), x)

________________________________________________________________________________________

Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{arcoth}\left (\tan \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(arccoth(tan(b*x+a))/(f*x+e),x, algorithm="giac")

[Out]

integrate(arccoth(tan(b*x + a))/(f*x + e), x)