Evaluate the following integral by making the given substitution:
∫ ((sec^2(1/x)) / (x^2))dx
u= (1/x)
Any and all help is much appreciated! Thanks so much in advance!
∫ ((sec^2(1/x)) / (x^2))dx
u= (1/x)
Any and all help is much appreciated! Thanks so much in advance!
-
u = 1/x
=> du = -1/x^2 dx
=> ∫ ((sec^2(1/x)) / (x^2))dx = -∫ ((sec^2(u)) du
= -tan(u) +c
= - tan(1/x) +c which is the answer!
=> du = -1/x^2 dx
=> ∫ ((sec^2(1/x)) / (x^2))dx = -∫ ((sec^2(u)) du
= -tan(u) +c
= - tan(1/x) +c which is the answer!
-
∫ ((sec^2(1/x)) / (x^2))dx =
- ∫ ((sec^2(1/x)) d(1/x) = - tan(1/x)+C
- ∫ ((sec^2(1/x)) d(1/x) = - tan(1/x)+C