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

Optimal. Leaf size=20 \[ \text{Unintegrable}\left (\frac{a+b \tanh (e+f x)}{c+d x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.0309777, 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 = {} \[ \int \frac{a+b \tanh (e+f x)}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

Mathematica [A]  time = 4.13493, size = 0, normalized size = 0. \[ \int \frac{a+b \tanh (e+f x)}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.122, size = 0, normalized size = 0. \begin{align*} \int{\frac{a+b\tanh \left ( fx+e \right ) }{dx+c}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a+b*tanh(f*x+e))/(d*x+c),x)

[Out]

int((a+b*tanh(f*x+e))/(d*x+c),x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral((b*tanh(f*x + e) + a)/(d*x + c), x)

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

[Out]

Integral((a + 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{b \tanh \left (f x + e\right ) + a}{d x + c}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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