3.1.66 \(\int \frac {(a+b \tanh (e+f x))^3}{c+d x} \, dx\) [66]

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

[Out]

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

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Rubi [A]
time = 0.04, 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 {(a+b \tanh (e+f x))^3}{c+d x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 41.63, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(a+b \tanh (e+f x))^3}{c+d x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

a^3*log(d*x + c)/d + (3*a^2*b + 3*a*b^2 + b^3)*log(d*x + c)/d + (6*a*b^2*d*f*x + 6*a*b^2*c*f - b^3*d + (2*(3*a
*b^2*d*f + b^3*d*f)*x*e^(2*e) + (6*a*b^2*c*f + (2*c*f - d)*b^3)*e^(2*e))*e^(2*f*x))/(d^2*f^2*x^2 + 2*c*d*f^2*x
+ c^2*f^2 + (d^2*f^2*x^2*e^(4*e) + 2*c*d*f^2*x*e^(4*e) + c^2*f^2*e^(4*e))*e^(4*f*x) + 2*(d^2*f^2*x^2*e^(2*e)
+ 2*c*d*f^2*x*e^(2*e) + c^2*f^2*e^(2*e))*e^(2*f*x)) - integrate(2*(3*a^2*b*c^2*f^2 - 3*a*b^2*c*d*f + (c^2*f^2
+ d^2)*b^3 + (3*a^2*b*d^2*f^2 + b^3*d^2*f^2)*x^2 + (6*a^2*b*c*d*f^2 + 2*b^3*c*d*f^2 - 3*a*b^2*d^2*f)*x)/(d^3*f
^2*x^3 + 3*c*d^2*f^2*x^2 + 3*c^2*d*f^2*x + c^3*f^2 + (d^3*f^2*x^3*e^(2*e) + 3*c*d^2*f^2*x^2*e^(2*e) + 3*c^2*d*
f^2*x*e^(2*e) + c^3*f^2*e^(2*e))*e^(2*f*x)), x)

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Fricas [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((a+b*tanh(f*x+e))^3/(d*x+c),x, algorithm="fricas")

[Out]

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

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a + b \tanh {\left (e + f x \right )}\right )^{3}}{c + d x}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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