3.2.87 \(\int \frac {\cot ^{-1}(\tanh (a+b x))}{e+f x} \, dx\) [187]

Optimal. Leaf size=18 \[ \text {Int}\left (\frac {\cot ^{-1}(\tanh (a+b x))}{e+f x},x\right ) \]

[Out]

CannotIntegrate(arccot(tanh(b*x+a))/(f*x+e),x)

________________________________________________________________________________________

Rubi [A]
time = 0.03, 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 = {} \begin {gather*} \int \frac {\cot ^{-1}(\tanh (a+b x))}{e+f x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[ArcCot[Tanh[a + b*x]]/(e + f*x),x]

[Out]

Defer[Int][ArcCot[Tanh[a + b*x]]/(e + f*x), x]

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]
time = 5.54, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\cot ^{-1}(\tanh (a+b x))}{e+f x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[ArcCot[Tanh[a + b*x]]/(e + f*x),x]

[Out]

Integrate[ArcCot[Tanh[a + b*x]]/(e + f*x), x]

________________________________________________________________________________________

Maple [A]
time = 0.19, size = 0, normalized size = 0.00 \[\int \frac {\mathrm {arccot}\left (\tanh \left (b x +a \right )\right )}{f x +e}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(arccot(tanh(b*x+a))/(f*x+e),x)

[Out]

int(arccot(tanh(b*x+a))/(f*x+e),x)

________________________________________________________________________________________

Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(arccot(tanh(b*x + a))/(f*x + e), x)

________________________________________________________________________________________

Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(arccot(tanh(b*x + a))/(f*x + e), x)

________________________________________________________________________________________

Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\operatorname {acot}{\left (\tanh {\left (a + b x \right )} \right )}}{e + f x}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(acot(tanh(b*x+a))/(f*x+e),x)

[Out]

Integral(acot(tanh(a + b*x))/(e + f*x), x)

________________________________________________________________________________________

Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

sage0*x

________________________________________________________________________________________

Mupad [A]
time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int \frac {\mathrm {acot}\left (\mathrm {tanh}\left (a+b\,x\right )\right )}{e+f\,x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(acot(tanh(a + b*x))/(e + f*x),x)

[Out]

int(acot(tanh(a + b*x))/(e + f*x), x)

________________________________________________________________________________________