For the following integral find an appropriate TRIGONOMETRIC SUBSTITUTION of the form x=f(t) to simplify the integral.

INT (x)/(sqrt(-191-8x^2+80x))dx

x=?

2 answers

The integral will be of the form
(y+5)/sqrt(a^2-y^2)
if you complete the square of the expression under the square-root sign using
y=x-5, or x=y-5
That will reduce the given integral to two simpler ones.
sint