3.339 \(\int \frac {\tanh (a+b x)}{x} \, dx\)

Optimal. Leaf size=13 \[ \text {Int}\left (\frac {\tanh (a+b x)}{x},x\right ) \]

[Out]

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

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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 = {} \[ \int \frac {\tanh (a+b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Tanh[a + b*x]/x,x]

[Out]

Defer[Int][Tanh[a + b*x]/x, x]

Rubi steps

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

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Mathematica [A]  time = 12.31, size = 0, normalized size = 0.00 \[ \int \frac {\tanh (a+b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Tanh[a + b*x]/x,x]

[Out]

Integrate[Tanh[a + b*x]/x, x]

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fricas [A]  time = 0.49, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {sech}\left (b x + a\right ) \sinh \left (b x + a\right )}{x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.33, size = 0, normalized size = 0.00 \[ \int \frac {\mathrm {sech}\left (b x +a \right ) \sinh \left (b x +a \right )}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [A]  time = 0.00, size = -1, normalized size = -0.08 \[ \int \frac {\mathrm {sinh}\left (a+b\,x\right )}{x\,\mathrm {cosh}\left (a+b\,x\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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