3.1.10 \(\int \frac {\tanh ^2(e+f x)}{(c+d x)^2} \, dx\) [10]

Optimal. Leaf size=19 \[ \text {Int}\left (\frac {\tanh ^2(e+f x)}{(c+d x)^2},x\right ) \]

[Out]

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

________________________________________________________________________________________

Rubi [A]
time = 0.02, 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 {\tanh ^2(e+f x)}{(c+d x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Tanh[e + f*x]^2/(c + d*x)^2,x]

[Out]

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

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]
time = 16.65, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\tanh ^2(e+f x)}{(c+d x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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

[Out]

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

________________________________________________________________________________________

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(tanh(f*x+e)^2/(d*x+c)^2,x, algorithm="fricas")

[Out]

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

________________________________________________________________________________________

Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\tanh ^{2}{\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(tanh(f*x+e)**2/(d*x+c)**2,x)

[Out]

Integral(tanh(e + f*x)**2/(c + d*x)**2, x)

________________________________________________________________________________________

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

[Out]

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

________________________________________________________________________________________

Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {{\mathrm {tanh}\left (e+f\,x\right )}^2}{{\left (c+d\,x\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(tanh(e + f*x)^2/(c + d*x)^2,x)

[Out]

int(tanh(e + f*x)^2/(c + d*x)^2, x)

________________________________________________________________________________________