3.1.22 \(\int (c+d x)^2 \sqrt {b \tanh (e+f x)} \, dx\) [22]

Optimal. Leaf size=23 \[ \text {Int}\left ((c+d x)^2 \sqrt {b \tanh (e+f x)},x\right ) \]

[Out]

Unintegrable((d*x+c)^2*(b*tanh(f*x+e))^(1/2),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 (c+d x)^2 \sqrt {b \tanh (e+f x)} \, dx \end {gather*}

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*}

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Mathematica [F]
time = 180.00, size = 0, normalized size = 0.00 \begin {gather*} \text {\$Aborted} \end {gather*}

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 = 180.00, size = 0, normalized size = 0.00 \[\int \left (d x +c \right )^{2} \sqrt {b \tanh \left (f x +e \right )}\, dx\]

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 = 0.00, 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((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 = 0.00, 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((d*x+c)^2*(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)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \sqrt {b \tanh {\left (e + f x \right )}} \left (c + d x\right )^{2}\, dx \end {gather*}

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)

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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((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)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \sqrt {b\,\mathrm {tanh}\left (e+f\,x\right )}\,{\left (c+d\,x\right )}^2 \,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)^2,x)

[Out]

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

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