Integrand size = 26, antiderivative size = 26 \[ \int \frac {x}{\left (1-c^2 x^2\right )^{3/2} (a+b \text {arccosh}(c x))^2} \, dx=\text {Int}\left (\frac {x}{\left (1-c^2 x^2\right )^{3/2} (a+b \text {arccosh}(c x))^2},x\right ) \]
[Out]
Not integrable
Time = 0.08 (sec) , antiderivative size = 26, 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 = {} \[ \int \frac {x}{\left (1-c^2 x^2\right )^{3/2} (a+b \text {arccosh}(c x))^2} \, dx=\int \frac {x}{\left (1-c^2 x^2\right )^{3/2} (a+b \text {arccosh}(c x))^2} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {x}{\left (1-c^2 x^2\right )^{3/2} (a+b \text {arccosh}(c x))^2} \, dx \\ \end{align*}
Not integrable
Time = 19.57 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08 \[ \int \frac {x}{\left (1-c^2 x^2\right )^{3/2} (a+b \text {arccosh}(c x))^2} \, dx=\int \frac {x}{\left (1-c^2 x^2\right )^{3/2} (a+b \text {arccosh}(c x))^2} \, dx \]
[In]
[Out]
Not integrable
Time = 1.12 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92
\[\int \frac {x}{\left (-c^{2} x^{2}+1\right )^{\frac {3}{2}} \left (a +b \,\operatorname {arccosh}\left (c x \right )\right )^{2}}d x\]
[In]
[Out]
Not integrable
Time = 0.26 (sec) , antiderivative size = 104, normalized size of antiderivative = 4.00 \[ \int \frac {x}{\left (1-c^2 x^2\right )^{3/2} (a+b \text {arccosh}(c x))^2} \, dx=\int { \frac {x}{{\left (-c^{2} x^{2} + 1\right )}^{\frac {3}{2}} {\left (b \operatorname {arcosh}\left (c x\right ) + a\right )}^{2}} \,d x } \]
[In]
[Out]
Not integrable
Time = 59.91 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.04 \[ \int \frac {x}{\left (1-c^2 x^2\right )^{3/2} (a+b \text {arccosh}(c x))^2} \, dx=\int \frac {x}{\left (- \left (c x - 1\right ) \left (c x + 1\right )\right )^{\frac {3}{2}} \left (a + b \operatorname {acosh}{\left (c x \right )}\right )^{2}}\, dx \]
[In]
[Out]
Not integrable
Time = 0.93 (sec) , antiderivative size = 511, normalized size of antiderivative = 19.65 \[ \int \frac {x}{\left (1-c^2 x^2\right )^{3/2} (a+b \text {arccosh}(c x))^2} \, dx=\int { \frac {x}{{\left (-c^{2} x^{2} + 1\right )}^{\frac {3}{2}} {\left (b \operatorname {arcosh}\left (c x\right ) + a\right )}^{2}} \,d x } \]
[In]
[Out]
Exception generated. \[ \int \frac {x}{\left (1-c^2 x^2\right )^{3/2} (a+b \text {arccosh}(c x))^2} \, dx=\text {Exception raised: TypeError} \]
[In]
[Out]
Not integrable
Time = 3.59 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00 \[ \int \frac {x}{\left (1-c^2 x^2\right )^{3/2} (a+b \text {arccosh}(c x))^2} \, dx=\int \frac {x}{{\left (a+b\,\mathrm {acosh}\left (c\,x\right )\right )}^2\,{\left (1-c^2\,x^2\right )}^{3/2}} \,d x \]
[In]
[Out]