3.14 \(\int \frac {\tanh ^3(e+f x)}{c+d x} \, dx\)

Optimal. Leaf size=19 \[ \text {Int}\left (\frac {\tanh ^3(e+f x)}{c+d x},x\right ) \]

[Out]

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

________________________________________________________________________________________

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

Verification is Not applicable to the result.

[In]

Int[Tanh[e + f*x]^3/(c + d*x),x]

[Out]

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

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]  time = 31.07, size = 0, normalized size = 0.00 \[ \int \frac {\tanh ^3(e+f x)}{c+d x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

________________________________________________________________________________________

fricas [A]  time = 0.55, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\tanh \left (f x + e\right )^{3}}{d x + c}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(tanh(f*x+e)^3/(d*x+c),x, algorithm="fricas")

[Out]

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

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

maple [A]  time = 0.81, size = 0, normalized size = 0.00 \[ \int \frac {\tanh ^{3}\left (f x +e \right )}{d x +c}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \frac {{\left (2 \, d f x e^{\left (2 \, e\right )} + 2 \, c f e^{\left (2 \, e\right )} - d e^{\left (2 \, e\right )}\right )} e^{\left (2 \, f x\right )} - d}{d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + {\left (d^{2} f^{2} x^{2} e^{\left (4 \, e\right )} + 2 \, c d f^{2} x e^{\left (4 \, e\right )} + c^{2} f^{2} e^{\left (4 \, e\right )}\right )} e^{\left (4 \, f x\right )} + 2 \, {\left (d^{2} f^{2} x^{2} e^{\left (2 \, e\right )} + 2 \, c d f^{2} x e^{\left (2 \, e\right )} + c^{2} f^{2} e^{\left (2 \, e\right )}\right )} e^{\left (2 \, f x\right )}} + \frac {\log \left (d x + c\right )}{d} - \int \frac {2 \, {\left (d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + d^{2}\right )}}{d^{3} f^{2} x^{3} + 3 \, c d^{2} f^{2} x^{2} + 3 \, c^{2} d f^{2} x + c^{3} f^{2} + {\left (d^{3} f^{2} x^{3} e^{\left (2 \, e\right )} + 3 \, c d^{2} f^{2} x^{2} e^{\left (2 \, e\right )} + 3 \, c^{2} d f^{2} x e^{\left (2 \, e\right )} + c^{3} f^{2} e^{\left (2 \, e\right )}\right )} e^{\left (2 \, f x\right )}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

((2*d*f*x*e^(2*e) + 2*c*f*e^(2*e) - d*e^(2*e))*e^(2*f*x) - d)/(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)) + log(d*x + c)/d - integrate(2*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + d^2)/(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)

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {{\mathrm {tanh}\left (e+f\,x\right )}^3}{c+d\,x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(tanh(e + f*x)^3/(c + d*x),x)

[Out]

int(tanh(e + f*x)^3/(c + d*x), x)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(tanh(e + f*x)**3/(c + d*x), x)

________________________________________________________________________________________