3.1.55 \(\int \frac {1}{(c+d x) (a+b \coth (e+f x))} \, dx\) [55]

Optimal. Leaf size=23 \[ \text {Int}\left (\frac {1}{(c+d x) (a+b \coth (e+f x))},x\right ) \]

[Out]

Unintegrable(1/(d*x+c)/(a+b*coth(f*x+e)),x)

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Rubi [A]
time = 0.04, 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 {1}{(c+d x) (a+b \coth (e+f x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[1/((c + d*x)*(a + b*Coth[e + f*x])),x]

[Out]

Defer[Int][1/((c + d*x)*(a + b*Coth[e + f*x])), x]

Rubi steps

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

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Mathematica [A]
time = 9.90, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{(c+d x) (a+b \coth (e+f x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[1/((c + d*x)*(a + b*Coth[e + f*x])),x]

[Out]

Integrate[1/((c + d*x)*(a + b*Coth[e + f*x])), x]

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Maple [A]
time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (d x +c \right ) \left (a +b \coth \left (f x +e \right )\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(d*x+c)/(a+b*coth(f*x+e)),x)

[Out]

int(1/(d*x+c)/(a+b*coth(f*x+e)),x)

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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(1/(d*x+c)/(a+b*coth(f*x+e)),x, algorithm="maxima")

[Out]

-2*b*integrate(-1/(a^2*c - b^2*c + (a^2*d - b^2*d)*x - ((a^2*d + 2*a*b*d + b^2*d)*x*e^(2*e) + (a^2*c + 2*a*b*c
+ b^2*c)*e^(2*e))*e^(2*f*x)), x) + log(d*x + c)/(a*d + b*d)

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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(1/(d*x+c)/(a+b*coth(f*x+e)),x, algorithm="fricas")

[Out]

integral(1/(a*d*x + a*c + (b*d*x + b*c)*coth(f*x + e)), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (a + b \coth {\left (e + f x \right )}\right ) \left (c + d x\right )}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(d*x+c)/(a+b*coth(f*x+e)),x)

[Out]

Integral(1/((a + b*coth(e + f*x))*(c + d*x)), x)

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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(1/(d*x+c)/(a+b*coth(f*x+e)),x, algorithm="giac")

[Out]

integrate(1/((d*x + c)*(b*coth(f*x + e) + a)), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {1}{\left (a+b\,\mathrm {coth}\left (e+f\,x\right )\right )\,\left (c+d\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((a + b*coth(e + f*x))*(c + d*x)),x)

[Out]

int(1/((a + b*coth(e + f*x))*(c + d*x)), x)

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