3.1.28 \(\int \frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx\) [28]

Optimal. Leaf size=23 \[ \text {Int}\left (\frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}},x\right ) \]

[Out]

Unintegrable(1/(d*x+c)/(b*tanh(f*x+e))^(3/2),x)

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Rubi [A]
time = 0.05, 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 \frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[1/((c + d*x)*(b*Tanh[e + f*x])^(3/2)),x]

[Out]

Defer[Int][1/((c + d*x)*(b*Tanh[e + f*x])^(3/2)), x]

Rubi steps

\begin {align*} \int \frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx &=\int \frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx\\ \end {align*}

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Mathematica [A]
time = 17.02, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[1/((c + d*x)*(b*Tanh[e + f*x])^(3/2)),x]

[Out]

Integrate[1/((c + d*x)*(b*Tanh[e + f*x])^(3/2)), x]

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Maple [A]
time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (d x +c \right ) \left (b \tanh \left (f x +e \right )\right )^{\frac {3}{2}}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(d*x+c)/(b*tanh(f*x+e))^(3/2),x)

[Out]

int(1/(d*x+c)/(b*tanh(f*x+e))^(3/2),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(1/(d*x+c)/(b*tanh(f*x+e))^(3/2),x, algorithm="maxima")

[Out]

integrate(1/((d*x + c)*(b*tanh(f*x + e))^(3/2)), 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(1/(d*x+c)/(b*tanh(f*x+e))^(3/2),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 \frac {1}{\left (b \tanh {\left (e + f x \right )}\right )^{\frac {3}{2}} \left (c + d x\right )}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(d*x+c)/(b*tanh(f*x+e))**(3/2),x)

[Out]

Integral(1/((b*tanh(e + f*x))**(3/2)*(c + d*x)), 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(1/(d*x+c)/(b*tanh(f*x+e))^(3/2),x, algorithm="giac")

[Out]

integrate(1/((d*x + c)*(b*tanh(f*x + e))^(3/2)), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {1}{{\left (b\,\mathrm {tanh}\left (e+f\,x\right )\right )}^{3/2}\,\left (c+d\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((b*tanh(e + f*x))^(3/2)*(c + d*x)),x)

[Out]

int(1/((b*tanh(e + f*x))^(3/2)*(c + d*x)), x)

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