3.1.27 \(\int \frac {1}{(c+d x) \sqrt {b \tanh (e+f x)}} \, dx\) [27]

Optimal. Leaf size=23 \[ \text {Int}\left (\frac {1}{(c+d x) \sqrt {b \tanh (e+f x)}},x\right ) \]

[Out]

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

________________________________________________________________________________________

Rubi [A]
time = 0.04, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {1}{(c+d x) \sqrt {b \tanh (e+f x)}} \, dx \end {gather*}

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 = 1.62, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{(c+d x) \sqrt {b \tanh (e+f x)}} \, dx \end {gather*}

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]

________________________________________________________________________________________

Maple [A]
time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (d x +c \right ) \sqrt {b \tanh \left (f x +e \right )}}\, dx\]

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)

________________________________________________________________________________________

Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

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)

________________________________________________________________________________________

Fricas [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}

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: TypeError >>  Error detected within library code:   integrate: implementation incomplete (co
nstant residues)

________________________________________________________________________________________

Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\sqrt {b \tanh {\left (e + f x \right )}} \left (c + d x\right )}\, dx \end {gather*}

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)

________________________________________________________________________________________

Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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)

________________________________________________________________________________________

Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {1}{\sqrt {b\,\mathrm {tanh}\left (e+f\,x\right )}\,\left (c+d\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________