Evaluate the following integrals


Let

Using sin 2x =2 sin x cos x, we get




Let tan x=t


sec2xdx=dt.


Also, when x=0, t=0


and when , t=∞.


Hence,


Let x2=t


2xdx=dt.


Also, when x=0, t=0


and when x=∞, t=∞.


Hence,




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