The integral of the function sqrt(x^2 - 1) can be evaluated using the substitution x = cosh(t), which leads to dx = sinh(t) dt. This method provides an alternative to the commonly used secant substitution. While sec(θ) substitution is effective, the hyperbolic substitution offers a different approach to solving the integral without relying on trigonometric identities.
PREREQUISITESStudents and educators in calculus, mathematicians exploring integration techniques, and anyone interested in advanced methods of solving integrals without traditional trigonometric substitutions.
What's the problem with letting x = sec(θ) ?physicsjock said:Is there a way to do this integral without substituting in sec?
int sqr(x^2-1)
Ive tried a bunch of things, but the only thing that works is using sec,
Is there any other method?