Formula to be used – We know,

Assuming x = tana,

And, dx = sec²ada

Hence, a=tan^-1x

Now, sec²a-tan²a=1 , so, seca=√(1+x²)

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) = a and f₂(x) = sec²a,

Replacing the value of a we get,

, where c is the integrating constant