In this video I go over the same example 5 on trig substitution for integrals which I did in my last video but this time solve it using hyperbolic trig substitution instead. Although using hyperbolic trig substitution in this example is more complicated, I wanted to illustrate that there were other methods of solving the same integral. The final answer we get using this method is in the form of an inverse hyperbolic trig function but when writing this function as a logarithmic function, we get the same answer as we did in my last video.

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Trigonometric Substitution for Integrals: Example 5 Part 2: Using hyperbolic trig substitution

In my last video I solved the following example:

I used the following trig substitution to solve it:

And the answer we got was:

If we only consider when x > 0, then another method of solving this example is by using the following hyperbolic trig substitution:

We need to ensure that a*cosh(t) has a one-to-one relationship while maintaining the domain of x > a

Note: As shown in this example, hyperbolic trig substitutions can be used in place of trig substitutions and sometimes they lead to simpler answers. But we usually use trig substitutions because trig functions and trig identities are more familiar than hyperbolic functions and identities.