3.26 \(\int \frac{\sqrt{b \tanh (e+f x)}}{c+d x} \, dx\)

Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{\sqrt{b \tanh (e+f x)}}{c+d x},x\right ) \]

[Out]

Unintegrable[Sqrt[b*Tanh[e + f*x]]/(c + d*x), x]

________________________________________________________________________________________

Rubi [A]  time = 0.0536525, 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 = {} \[ \int \frac{\sqrt{b \tanh (e+f x)}}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Sqrt[b*Tanh[e + f*x]]/(c + d*x),x]

[Out]

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

Rubi steps

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

Mathematica [A]  time = 1.9394, size = 0, normalized size = 0. \[ \int \frac{\sqrt{b \tanh (e+f x)}}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Sqrt[b*Tanh[e + f*x]]/(c + d*x),x]

[Out]

Integrate[Sqrt[b*Tanh[e + f*x]]/(c + d*x), x]

________________________________________________________________________________________

Maple [A]  time = 0.104, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{dx+c}\sqrt{b\tanh \left ( fx+e \right ) }}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*tanh(f*x+e))^(1/2)/(d*x+c),x)

[Out]

int((b*tanh(f*x+e))^(1/2)/(d*x+c),x)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*tanh(f*x+e))^(1/2)/(d*x+c),x, algorithm="maxima")

[Out]

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

________________________________________________________________________________________

Fricas [F(-2)]  time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*tanh(f*x+e))^(1/2)/(d*x+c),x, algorithm="fricas")

[Out]

Exception raised: UnboundLocalError

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*tanh(f*x+e))**(1/2)/(d*x+c),x)

[Out]

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

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*tanh(f*x+e))^(1/2)/(d*x+c),x, algorithm="giac")

[Out]

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