3.40 \(\int \frac {a+b \coth (e+f x)}{c+d x} \, dx\)

Optimal. Leaf size=21 \[ \text {Int}\left (\frac {a+b \coth (e+f x)}{c+d x},x\right ) \]

[Out]

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

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

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 5.32, size = 0, normalized size = 0.00 \[ \int \frac {a+b \coth (e+f x)}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.39, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {b \coth \left (f x + e\right ) + a}{d x + c}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.58, size = 0, normalized size = 0.00 \[ \int \frac {a +b \coth \left (f x +e \right )}{d x +c}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ b {\left (\frac {\log \left (d x + c\right )}{d} - \int \frac {1}{d x + {\left (d x e^{e} + c e^{e}\right )} e^{\left (f x\right )} + c}\,{d x} + \int -\frac {1}{d x - {\left (d x e^{e} + c e^{e}\right )} e^{\left (f x\right )} + c}\,{d x}\right )} + \frac {a \log \left (d x + c\right )}{d} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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