### 3.368 $$\int \frac{\tanh ^2(a+b x)}{x^2} \, dx$$

Optimal. Leaf size=14 $\text{Unintegrable}\left (\frac{\tanh ^2(a+b x)}{x^2},x\right )$

[Out]

Unintegrable[Tanh[a + b*x]^2/x^2, x]

________________________________________________________________________________________

Rubi [A]  time = 0.0303789, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, $$\frac{\text{number of rules}}{\text{integrand size}}$$ = 0., Rules used = {} $\int \frac{\tanh ^2(a+b x)}{x^2} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Int[Tanh[a + b*x]^2/x^2,x]

[Out]

Defer[Int][Tanh[a + b*x]^2/x^2, x]

Rubi steps

\begin{align*} \int \frac{\tanh ^2(a+b x)}{x^2} \, dx &=\int \frac{\tanh ^2(a+b x)}{x^2} \, dx\\ \end{align*}

Mathematica [A]  time = 11.6612, size = 0, normalized size = 0. $\int \frac{\tanh ^2(a+b x)}{x^2} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Integrate[Tanh[a + b*x]^2/x^2,x]

[Out]

Integrate[Tanh[a + b*x]^2/x^2, x]

________________________________________________________________________________________

Maple [A]  time = 0.066, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\rm sech} \left (bx+a\right ) \right ) ^{2} \left ( \sinh \left ( bx+a \right ) \right ) ^{2}}{{x}^{2}}}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(sech(b*x+a)^2*sinh(b*x+a)^2/x^2,x)

[Out]

int(sech(b*x+a)^2*sinh(b*x+a)^2/x^2,x)

________________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{b x e^{\left (2 \, b x + 2 \, a\right )} + b x - 2}{b x^{2} e^{\left (2 \, b x + 2 \, a\right )} + b x^{2}} + 4 \, \int \frac{1}{b x^{3} e^{\left (2 \, b x + 2 \, a\right )} + b x^{3}}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(sech(b*x+a)^2*sinh(b*x+a)^2/x^2,x, algorithm="maxima")

[Out]

-(b*x*e^(2*b*x + 2*a) + b*x - 2)/(b*x^2*e^(2*b*x + 2*a) + b*x^2) + 4*integrate(1/(b*x^3*e^(2*b*x + 2*a) + b*x^
3), x)

________________________________________________________________________________________

Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\operatorname{sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )^{2}}{x^{2}}, x\right ) \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(sech(b*x+a)^2*sinh(b*x+a)^2/x^2,x, algorithm="fricas")

[Out]

integral(sech(b*x + a)^2*sinh(b*x + a)^2/x^2, x)

________________________________________________________________________________________

Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sinh ^{2}{\left (a + b x \right )} \operatorname{sech}^{2}{\left (a + b x \right )}}{x^{2}}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(sech(b*x+a)**2*sinh(b*x+a)**2/x**2,x)

[Out]

Integral(sinh(a + b*x)**2*sech(a + b*x)**2/x**2, x)

________________________________________________________________________________________

Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )^{2}}{x^{2}}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(sech(b*x+a)^2*sinh(b*x+a)^2/x^2,x, algorithm="giac")

[Out]

integrate(sech(b*x + a)^2*sinh(b*x + a)^2/x^2, x)