- #1

- 565

- 2

(tdt)/(4-t^4)^(1/2)

Attempt:

I want the derivate of whatever i make u equal to, to equal something outside of u therefore I will factorize the denominator to equal -(-2+t^2)(2+t^2) and make u equal to (2+t^2) so that du=2tdt

Balance the equation so that one side is equal to the numerator

(1/2)du=tdt

Now I have

1/2[tex]\int[/tex] = 1/(-(-2+t^2)u)^1/2

How do I apply this elementary integral in this situation?:

[tex]\int[/tex] 1/(a^2-x^2)^1/2 dx = sin^-1(x/a) + C

I don't know what to do with the u in

1/(-(-2+t^2)u)^1/2

If it helps the final answer is supposed to be:

(1/2)sin^-1(t^2/2)