Integrand size = 12, antiderivative size = 12 \[ \int \frac {x}{a+b \text {sech}^{-1}(c x)} \, dx=\text {Int}\left (\frac {x}{a+b \text {sech}^{-1}(c x)},x\right ) \]
[Out]
Not integrable
Time = 0.01 (sec) , antiderivative size = 12, 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 = {} \[ \int \frac {x}{a+b \text {sech}^{-1}(c x)} \, dx=\int \frac {x}{a+b \text {sech}^{-1}(c x)} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {x}{a+b \text {sech}^{-1}(c x)} \, dx \\ \end{align*}
Not integrable
Time = 2.99 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {x}{a+b \text {sech}^{-1}(c x)} \, dx=\int \frac {x}{a+b \text {sech}^{-1}(c x)} \, dx \]
[In]
[Out]
Not integrable
Time = 0.34 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00
\[\int \frac {x}{a +b \,\operatorname {arcsech}\left (c x \right )}d x\]
[In]
[Out]
Not integrable
Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {x}{a+b \text {sech}^{-1}(c x)} \, dx=\int { \frac {x}{b \operatorname {arsech}\left (c x\right ) + a} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.26 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {x}{a+b \text {sech}^{-1}(c x)} \, dx=\int \frac {x}{a + b \operatorname {asech}{\left (c x \right )}}\, dx \]
[In]
[Out]
Not integrable
Time = 0.29 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {x}{a+b \text {sech}^{-1}(c x)} \, dx=\int { \frac {x}{b \operatorname {arsech}\left (c x\right ) + a} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {x}{a+b \text {sech}^{-1}(c x)} \, dx=\int { \frac {x}{b \operatorname {arsech}\left (c x\right ) + a} \,d x } \]
[In]
[Out]
Not integrable
Time = 4.18 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.50 \[ \int \frac {x}{a+b \text {sech}^{-1}(c x)} \, dx=\int \frac {x}{a+b\,\mathrm {acosh}\left (\frac {1}{c\,x}\right )} \,d x \]
[In]
[Out]