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

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

[Out]

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

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Rubi [A]  time = 0.06, 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 = {} \[ \int \frac {(c+d x)^2}{\sqrt {b \tanh (e+f x)}} \, dx \]

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*}

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

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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fricas [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]

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

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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maple [A]  time = 0.22, size = 0, normalized size = 0.00 \[ \int \frac {\left (d x +c \right )^{2}}{\sqrt {b \tanh \left (f x +e \right )}}\, dx \]

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 \[ \int \frac {{\left (d x + c\right )}^{2}}{\sqrt {b \tanh \left (f x + e\right )}}\,{d x} \]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

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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