3.27 \(\int \frac{1}{(c+d x) \sqrt{b \tanh (e+f x)}} \, dx\)

Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{1}{(c+d x) \sqrt{b \tanh (e+f x)}},x\right ) \]

[Out]

Unintegrable[1/((c + d*x)*Sqrt[b*Tanh[e + f*x]]), x]

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Rubi [A]  time = 0.0591075, 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 = {} \[ \int \frac{1}{(c+d x) \sqrt{b \tanh (e+f x)}} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/((c + d*x)*Sqrt[b*Tanh[e + f*x]]),x]

[Out]

Defer[Int][1/((c + d*x)*Sqrt[b*Tanh[e + f*x]]), x]

Rubi steps

\begin{align*} \int \frac{1}{(c+d x) \sqrt{b \tanh (e+f x)}} \, dx &=\int \frac{1}{(c+d x) \sqrt{b \tanh (e+f x)}} \, dx\\ \end{align*}

Mathematica [A]  time = 2.23657, size = 0, normalized size = 0. \[ \int \frac{1}{(c+d x) \sqrt{b \tanh (e+f x)}} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/((c + d*x)*Sqrt[b*Tanh[e + f*x]]),x]

[Out]

Integrate[1/((c + d*x)*Sqrt[b*Tanh[e + f*x]]), x]

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Maple [A]  time = 0.12, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{dx+c}{\frac{1}{\sqrt{b\tanh \left ( fx+e \right ) }}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

[Out]

Exception raised: UnboundLocalError

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(1/(sqrt(b*tanh(e + f*x))*(c + d*x)), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (d x + c\right )} \sqrt{b \tanh \left (f x + e\right )}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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