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

Optimal. Leaf size=15 \[ \text {Int}\left (\frac {\tanh ^2(a+b x)}{x},x\right ) \]

[Out]

Unintegrable(tanh(b*x+a)^2/x,x)

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Rubi [A]  time = 0.03, 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 = {} \[ \int \frac {\tanh ^2(a+b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Tanh[a + b*x]^2/x,x]

[Out]

Defer[Int][Tanh[a + b*x]^2/x, x]

Rubi steps

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

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Mathematica [A]  time = 18.88, size = 0, normalized size = 0.00 \[ \int \frac {\tanh ^2(a+b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Tanh[a + b*x]^2/x,x]

[Out]

Integrate[Tanh[a + b*x]^2/x, x]

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fricas [A]  time = 0.65, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )^{2}}{x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {sech}\left (b x + a\right )^{2} \sinh \left (b x + a\right )^{2}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.59, size = 0, normalized size = 0.00 \[ \int \frac {\mathrm {sech}\left (b x +a \right )^{2} \left (\sinh ^{2}\left (b x +a \right )\right )}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \frac {2}{b x e^{\left (2 \, b x + 2 \, a\right )} + b x} + 2 \, \int \frac {1}{b x^{2} e^{\left (2 \, b x + 2 \, a\right )} + b x^{2}}\,{d x} + \log \relax (x) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2/(b*x*e^(2*b*x + 2*a) + b*x) + 2*integrate(1/(b*x^2*e^(2*b*x + 2*a) + b*x^2), x) + log(x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {{\mathrm {sinh}\left (a+b\,x\right )}^2}{x\,{\mathrm {cosh}\left (a+b\,x\right )}^2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sinh ^{2}{\left (a + b x \right )} \operatorname {sech}^{2}{\left (a + b x \right )}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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