How do you integrate ∫1√x2−16x−7 using trigonometric substitution?
1 Answer
Explanation:
Complete the square under the root:
Substitute:
so:
Restrict now to the interval
with
As
undoing the substitution:
and using the logarithmic form of the inverse hyperbolic cosine:
Multiplying the argument of the logarithm by
and by differentiating we can verify that the solution is valid also for