Question

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

INT((4x^2-3)^1.5) dx x=?

Answer 1

u = 4x^2 -3
(1/8)du = x dx
(1/8)INT u^(3/2) du
(1/8)(2/5)u^(5/2)
(1/20)(4x^2 -3)^(5/2)

I don't see why they demand a trigonometric solution. This seems like the logical one to use.

Answer 2

No it is required to use a trignometric substitution. x cannot be a variable in the final answer

Answer 3

you can do like this:
(4x^2-3)^1.5 = (4x^2-3).sq(4x^2-3)dx
Let 2x = Sq3.sec(det)
so, 4x^2 -3 = 3.sec^2(det)-3
= 3.tan^2(det)
new INT= INt(3^1.5tan^3(det)d(det)
Use Pythagore to solve the relation between x and the angle det.