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

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

[Out]

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

________________________________________________________________________________________

Rubi [A]  time = 0.0507774, 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 = {} \[ \int (c+d x)^2 \sqrt{b \tanh (e+f x)} \, dx \]

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

Mathematica [F]  time = 180.002, 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

________________________________________________________________________________________

Maple [A]  time = 0.096, size = 0, normalized size = 0. \begin{align*} \int \left ( dx+c \right ) ^{2}\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)

________________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int{\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)

________________________________________________________________________________________

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

________________________________________________________________________________________

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

________________________________________________________________________________________

Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int{\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)