Definite integral from 2sqrt(2) to 4 of 1/(t^3sqrt(t^2-4)) by trigonometric substitution?

trigonometric

#1

definite integral from 2sqrt(2) to 4 of 1/(t^3sqrt(t^2-4)) by trigonometric substitution?

Answer:

let, t=2 sec z

then dt= 2 sec z tan z dz

subsitute t and dt in the integral.

we only cos^2 z left
coos^2 z =1/2*(1+cos 2z)
then do the integration
substitute the value of z finall, z=sec^-1 t/2