Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{a+b \coth (e+f x)}{(c+d x)^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0288114, 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 = {} \[ \int \frac{a+b \coth (e+f x)}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{a+b \coth (e+f x)}{(c+d x)^2} \, dx &=\int \frac{a+b \coth (e+f x)}{(c+d x)^2} \, dx\\ \end{align*}
Mathematica [A] time = 20.337, size = 0, normalized size = 0. \[ \int \frac{a+b \coth (e+f x)}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.134, size = 0, normalized size = 0. \begin{align*} \int{\frac{a+b{\rm coth} \left (fx+e\right )}{ \left ( dx+c \right ) ^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} -b{\left (\frac{1}{d^{2} x + c d} + \int \frac{1}{d^{2} x^{2} + 2 \, c d x + c^{2} +{\left (d^{2} x^{2} e^{e} + 2 \, c d x e^{e} + c^{2} e^{e}\right )} e^{\left (f x\right )}}\,{d x} - \int -\frac{1}{d^{2} x^{2} + 2 \, c d x + c^{2} -{\left (d^{2} x^{2} e^{e} + 2 \, c d x e^{e} + c^{2} e^{e}\right )} e^{\left (f x\right )}}\,{d x}\right )} - \frac{a}{d^{2} x + c d} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{b \coth \left (f x + e\right ) + a}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{a + b \coth{\left (e + f x \right )}}{\left (c + d x\right )^{2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{b \coth \left (f x + e\right ) + a}{{\left (d x + c\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]