Question

∫ (1/x^2)[cos^2(1/x)]dx

Evaluate using substitution method?

Answer 1

\[\int\limits (1/x^2)[\cos^2(1/x)] dx\]

Answer 2

put 1/x = t
then differentiate this equation
to obtain
-1/x^2 dx = dt

Answer 3

annd then? :)

Answer 4

then replace values in the equation
1/x by t
and 1/x^2 by - dt

Answer 5

express cos^2x in terms of cos x

Answer 6

then integrate

Answer 7

cos^2t=(cos2t+1)/2

Answer 8

yup

Answer 9

and after integrating replace t by 1/x

Answer 10

what happens with the dx? aren't we supposed to replace that too?