Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{1}{(c+d x) (a+b \coth (e+f x))^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0619273, 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 = {} \[ \int \frac{1}{(c+d x) (a+b \coth (e+f x))^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{1}{(c+d x) (a+b \coth (e+f x))^2} \, dx &=\int \frac{1}{(c+d x) (a+b \coth (e+f x))^2} \, dx\\ \end{align*}
Mathematica [A] time = 144.035, size = 0, normalized size = 0. \[ \int \frac{1}{(c+d x) (a+b \coth (e+f x))^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.752, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{ \left ( dx+c \right ) \left ( a+b{\rm coth} \left (fx+e\right ) \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*} \frac{2 \, b^{2}}{a^{4} c f - 2 \, a^{2} b^{2} c f + b^{4} c f +{\left (a^{4} d f - 2 \, a^{2} b^{2} d f + b^{4} d f\right )} x -{\left (a^{4} c f e^{\left (2 \, e\right )} + 2 \, a^{3} b c f e^{\left (2 \, e\right )} - 2 \, a b^{3} c f e^{\left (2 \, e\right )} - b^{4} c f e^{\left (2 \, e\right )} +{\left (a^{4} d f e^{\left (2 \, e\right )} + 2 \, a^{3} b d f e^{\left (2 \, e\right )} - 2 \, a b^{3} d f e^{\left (2 \, e\right )} - b^{4} d f e^{\left (2 \, e\right )}\right )} x\right )} e^{\left (2 \, f x\right )}} + \frac{\log \left (d x + c\right )}{a^{2} d + 2 \, a b d + b^{2} d} - \int -\frac{2 \,{\left (2 \, a b d f x + 2 \, a b c f + b^{2} d\right )}}{a^{4} c^{2} f - 2 \, a^{2} b^{2} c^{2} f + b^{4} c^{2} f +{\left (a^{4} d^{2} f - 2 \, a^{2} b^{2} d^{2} f + b^{4} d^{2} f\right )} x^{2} + 2 \,{\left (a^{4} c d f - 2 \, a^{2} b^{2} c d f + b^{4} c d f\right )} x -{\left (a^{4} c^{2} f e^{\left (2 \, e\right )} + 2 \, a^{3} b c^{2} f e^{\left (2 \, e\right )} - 2 \, a b^{3} c^{2} f e^{\left (2 \, e\right )} - b^{4} c^{2} f e^{\left (2 \, e\right )} +{\left (a^{4} d^{2} f e^{\left (2 \, e\right )} + 2 \, a^{3} b d^{2} f e^{\left (2 \, e\right )} - 2 \, a b^{3} d^{2} f e^{\left (2 \, e\right )} - b^{4} d^{2} f e^{\left (2 \, e\right )}\right )} x^{2} + 2 \,{\left (a^{4} c d f e^{\left (2 \, e\right )} + 2 \, a^{3} b c d f e^{\left (2 \, e\right )} - 2 \, a b^{3} c d f e^{\left (2 \, e\right )} - b^{4} c d f e^{\left (2 \, e\right )}\right )} x\right )} e^{\left (2 \, f x\right )}}\,{d x} \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{1}{a^{2} d x + a^{2} c +{\left (b^{2} d x + b^{2} c\right )} \coth \left (f x + e\right )^{2} + 2 \,{\left (a b d x + a b c\right )} \coth \left (f x + e\right )}, 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{1}{\left (a + b \coth{\left (e + f x \right )}\right )^{2} \left (c + d x\right )}\, 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{1}{{\left (d x + c\right )}{\left (b \coth \left (f x + e\right ) + a\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]