3.23 \(\int \frac{(c+d x)^2}{\sqrt{b \tanh (e+f x)}} \, dx\)

Optimal. Leaf size=22 \[ \text{Unintegrable}\left (\frac{(c+d x)^2}{\sqrt{b \tanh (e+f x)}},x\right ) \]

[Out]

Unintegrable[(c + d*x)^2/Sqrt[b*Tanh[e + f*x]], x]

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Rubi [A]  time = 0.0554369, 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 = {} \[ \int \frac{(c+d x)^2}{\sqrt{b \tanh (e+f x)}} \, dx \]

Verification is Not applicable to the result.

[In]

Int[(c + d*x)^2/Sqrt[b*Tanh[e + f*x]],x]

[Out]

Defer[Int][(c + d*x)^2/Sqrt[b*Tanh[e + f*x]], x]

Rubi steps

\begin{align*} \int \frac{(c+d x)^2}{\sqrt{b \tanh (e+f x)}} \, dx &=\int \frac{(c+d x)^2}{\sqrt{b \tanh (e+f x)}} \, dx\\ \end{align*}

Mathematica [F]  time = 180.003, size = 0, normalized size = 0. \[ \text{\$Aborted} \]

Verification is Not applicable to the result.

[In]

Integrate[(c + d*x)^2/Sqrt[b*Tanh[e + f*x]],x]

[Out]

$Aborted

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Maple [A]  time = 0.101, size = 0, normalized size = 0. \begin{align*} \int{ \left ( dx+c \right ) ^{2}{\frac{1}{\sqrt{b\tanh \left ( fx+e \right ) }}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int((d*x+c)^2/(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{{\left (d x + c\right )}^{2}}{\sqrt{b \tanh \left (f x + e\right )}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate((d*x + c)^2/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((d*x+c)^2/(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{\left (c + d x\right )^{2}}{\sqrt{b \tanh{\left (e + f x \right )}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral((c + d*x)**2/sqrt(b*tanh(e + f*x)), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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