3.9 \(\int \frac{\tanh ^2(e+f x)}{c+d x} \, dx\)

Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\frac{\tanh ^2(e+f x)}{c+d x},x\right ) \]

[Out]

Unintegrable[Tanh[e + f*x]^2/(c + d*x), x]

________________________________________________________________________________________

Rubi [A]  time = 0.0365292, 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 = {} \[ \int \frac{\tanh ^2(e+f x)}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Tanh[e + f*x]^2/(c + d*x),x]

[Out]

Defer[Int][Tanh[e + f*x]^2/(c + d*x), x]

Rubi steps

\begin{align*} \int \frac{\tanh ^2(e+f x)}{c+d x} \, dx &=\int \frac{\tanh ^2(e+f x)}{c+d x} \, dx\\ \end{align*}

Mathematica [A]  time = 18.6926, size = 0, normalized size = 0. \[ \int \frac{\tanh ^2(e+f x)}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Tanh[e + f*x]^2/(c + d*x),x]

[Out]

Integrate[Tanh[e + f*x]^2/(c + d*x), x]

________________________________________________________________________________________

Maple [A]  time = 0.073, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( \tanh \left ( fx+e \right ) \right ) ^{2}}{dx+c}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(tanh(f*x+e)^2/(d*x+c),x)

[Out]

int(tanh(f*x+e)^2/(d*x+c),x)

________________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} 2 \, d \int \frac{1}{d^{2} f x^{2} + 2 \, c d f x + c^{2} f +{\left (d^{2} f x^{2} e^{\left (2 \, e\right )} + 2 \, c d f x e^{\left (2 \, e\right )} + c^{2} f e^{\left (2 \, e\right )}\right )} e^{\left (2 \, f x\right )}}\,{d x} + \frac{\log \left (d x + c\right )}{d} + \frac{2}{d f x + c f +{\left (d f x e^{\left (2 \, e\right )} + c f e^{\left (2 \, e\right )}\right )} e^{\left (2 \, f x\right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(tanh(f*x+e)^2/(d*x+c),x, algorithm="maxima")

[Out]

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

________________________________________________________________________________________

Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\tanh \left (f x + e\right )^{2}}{d x + c}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(tanh(f*x+e)^2/(d*x+c),x, algorithm="fricas")

[Out]

integral(tanh(f*x + e)^2/(d*x + c), x)

________________________________________________________________________________________

Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\tanh ^{2}{\left (e + f x \right )}}{c + d x}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(tanh(f*x+e)**2/(d*x+c),x)

[Out]

Integral(tanh(e + f*x)**2/(c + d*x), x)

________________________________________________________________________________________

Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\tanh \left (f x + e\right )^{2}}{d x + c}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(tanh(f*x+e)^2/(d*x+c),x, algorithm="giac")

[Out]

integrate(tanh(f*x + e)^2/(d*x + c), x)