Evaluate the following integrals:

Tip – If f₁(x) and f₂(x) are two functions , then an integral of the form can be INTEGRATED BY PARTS as

where f₁(x) and f₂(x) are the first and second functions respectively.

Taking f₁(x) = and f₂(x) = 1,

Now,

Again, we know,

Replacing x by tanx, it is obtained that,

So, the final integral yielded is

, where c is the integrating constant