Evaluate the following integral:

let us assume

let x = tany

differentiating both sides

dx = sec² y dy

for x = ∞

For x = 0

0 = y

thus

(since sec²y – tan²y = 1)

.....equation 1

By property, we know that

….....equation 2

Adding equations 1 and 2, we get,

We know

since logm + logn = logmn

since tany = 1/coty

since log 1 = 0

Thus

2I = 0

I = 0