Integrand size = 14, antiderivative size = 14 \[ \int \frac {1}{x (a+b \cosh (x) \sinh (x))} \, dx=\text {Int}\left (\frac {1}{x \left (a+\frac {1}{2} b \sinh (2 x)\right )},x\right ) \]
[Out]
Not integrable
Time = 0.06 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {1}{x (a+b \cosh (x) \sinh (x))} \, dx=\int \frac {1}{x (a+b \cosh (x) \sinh (x))} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{x \left (a+\frac {1}{2} b \sinh (2 x)\right )} \, dx \\ \end{align*}
Not integrable
Time = 0.96 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {1}{x (a+b \cosh (x) \sinh (x))} \, dx=\int \frac {1}{x (a+b \cosh (x) \sinh (x))} \, dx \]
[In]
[Out]
Not integrable
Time = 0.10 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00
\[\int \frac {1}{x \left (a +b \cosh \left (x \right ) \sinh \left (x \right )\right )}d x\]
[In]
[Out]
Not integrable
Time = 0.26 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07 \[ \int \frac {1}{x (a+b \cosh (x) \sinh (x))} \, dx=\int { \frac {1}{{\left (b \cosh \left (x\right ) \sinh \left (x\right ) + a\right )} x} \,d x } \]
[In]
[Out]
Not integrable
Time = 66.01 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {1}{x (a+b \cosh (x) \sinh (x))} \, dx=\int \frac {1}{x \left (a + b \sinh {\left (x \right )} \cosh {\left (x \right )}\right )}\, dx \]
[In]
[Out]
Not integrable
Time = 0.27 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {1}{x (a+b \cosh (x) \sinh (x))} \, dx=\int { \frac {1}{{\left (b \cosh \left (x\right ) \sinh \left (x\right ) + a\right )} x} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.26 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {1}{x (a+b \cosh (x) \sinh (x))} \, dx=\int { \frac {1}{{\left (b \cosh \left (x\right ) \sinh \left (x\right ) + a\right )} x} \,d x } \]
[In]
[Out]
Not integrable
Time = 2.29 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.14 \[ \int \frac {1}{x (a+b \cosh (x) \sinh (x))} \, dx=\int \frac {1}{x\,\left (a+b\,\mathrm {cosh}\left (x\right )\,\mathrm {sinh}\left (x\right )\right )} \,d x \]
[In]
[Out]