3.1.26 \(\int \frac {\sqrt {b \tanh (e+f x)}}{c+d x} \, dx\) [26]

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

[Out]

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

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Rubi [A]
time = 0.03, 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 {\sqrt {b \tanh (e+f x)}}{c+d x} \, dx \end {gather*}

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*}

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Mathematica [A]
time = 1.42, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {b \tanh (e+f x)}}{c+d x} \, dx \end {gather*}

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]

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

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)

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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((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)

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

[Out]

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

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

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)

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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((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)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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