MHB Solve Integration Problem - Get Help Now!

[NotaMathPerson]

Hello can you help solve this problem

$$\int_{}^{}\frac{ds}{\sqrt{s^2-0.01}}$$

I tried using method of substitution but I still could not find a good cancellation.
Please tell me what to do. Thanks!

 

[Dethrone]

Integrals of that form can be generalized to
$$\int \frac{ds}{\sqrt{s^2-r^2}}$$

Using the substitution $s=r \sec\left({x}\right)$ simplifies the integrand because of the property $\sec^2\left({x}\right)-1=\tan^2\left({x}\right)$.

Trying this, what do you get?

 

[Prove It]

The substitution $\displaystyle \begin{align*} s = r \cosh{(t)} \implies \mathrm{d}s = r\sinh{(t)}\,\mathrm{d}t \end{align*}$ may lead to a simpler integrand.