3.9.70 \(\int \frac {1}{x (a+b \cosh (x) \sinh (x))} \, dx\) [870]

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)

________________________________________________________________________________________

Rubi [A]
time = 0.06, 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 {1}{x (a+b \cosh (x) \sinh (x))} \, dx \end {gather*}

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*}

________________________________________________________________________________________

Mathematica [A]
time = 0.74, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x (a+b \cosh (x) \sinh (x))} \, dx \end {gather*}

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]

________________________________________________________________________________________

Maple [A]
time = 1.28, size = 0, normalized size = 0.00 \[\int \frac {1}{x \left (a +b \cosh \left (x \right ) \sinh \left (x \right )\right )}\, dx\]

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)

________________________________________________________________________________________

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

[Out]

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

[Out]

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

________________________________________________________________________________________

Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x \left (a + b \sinh {\left (x \right )} \cosh {\left (x \right )}\right )}\, dx \end {gather*}

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)

________________________________________________________________________________________

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

[Out]

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

________________________________________________________________________________________

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

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)

________________________________________________________________________________________