3.870 \(\int \frac {1}{x (a+b \cosh (x) \sinh (x))} \, dx\)

Optimal. Leaf size=20 \[ \text {Int}\left (\frac {1}{x \left (a+\frac {1}{2} b \sinh (2 x)\right )},x\right ) \]

[Out]

Unintegrable(1/x/(a+1/2*b*sinh(2*x)),x)

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Rubi [A]  time = 0.09, 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 = {} \[ \int \frac {1}{x (a+b \cosh (x) \sinh (x))} \, dx \]

Verification is Not applicable to the result.

[In]

Int[1/(x*(a + b*Cosh[x]*Sinh[x])),x]

[Out]

Defer[Int][1/(x*(a + (b*Sinh[2*x])/2)), x]

Rubi steps

\begin {align*} \int \frac {1}{x (a+b \cosh (x) \sinh (x))} \, dx &=\int \frac {1}{x \left (a+\frac {1}{2} b \sinh (2 x)\right )} \, dx\\ \end {align*}

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Mathematica [A]  time = 1.08, size = 0, normalized size = 0.00 \[ \int \frac {1}{x (a+b \cosh (x) \sinh (x))} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[1/(x*(a + b*Cosh[x]*Sinh[x])),x]

[Out]

Integrate[1/(x*(a + b*Cosh[x]*Sinh[x])), x]

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fricas [A]  time = 0.54, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{b x \cosh \relax (x) \sinh \relax (x) + a x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a+b*cosh(x)*sinh(x)),x, algorithm="fricas")

[Out]

integral(1/(b*x*cosh(x)*sinh(x) + a*x), x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{{\left (b \cosh \relax (x) \sinh \relax (x) + a\right )} x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a+b*cosh(x)*sinh(x)),x, algorithm="giac")

[Out]

integrate(1/((b*cosh(x)*sinh(x) + a)*x), x)

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maple [A]  time = 0.34, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \left (a +b \cosh \relax (x ) \sinh \relax (x )\right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x/(a+b*cosh(x)*sinh(x)),x)

[Out]

int(1/x/(a+b*cosh(x)*sinh(x)),x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a+b*cosh(x)*sinh(x)),x, algorithm="maxima")

[Out]

integrate(1/((b*cosh(x)*sinh(x) + a)*x), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {1}{x\,\left (a+b\,\mathrm {cosh}\relax (x)\,\mathrm {sinh}\relax (x)\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x*(a + b*cosh(x)*sinh(x))),x)

[Out]

int(1/(x*(a + b*cosh(x)*sinh(x))), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \left (a + b \sinh {\relax (x )} \cosh {\relax (x )}\right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x/(a+b*cosh(x)*sinh(x)),x)

[Out]

Integral(1/(x*(a + b*sinh(x)*cosh(x))), x)

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