# Integration by substitution, using $x=\csc(\theta)$

I have been given the integral in the top-left of the image.

I am fairly new to integration (I know basic integration with powers, how to use integration by substitution and what some trigonometric functions differentiate to) and got stuck trying to simplify this integral (I got up to the integral at the bottom).

Any hints would be great!

$$x=\csc t,dx=-\csc t\cot t\ dt$$
$$-\dfrac\pi2
$$\int\dfrac{dx}{x^2\sqrt{x^2-1}}=-\int\dfrac{\csc t\cot t}{\csc^2t\cot t}dt=-\int\sin t \ dt=K+\cos t$$
$$\cos t=\dfrac{\cot t}{\csc t}=?$$
• @Jamminermit, Actually I missed to put $$dt$$ – lab bhattacharjee Jul 12 at 18:40