Evaluate the following integrals:
[CBSE 2006C]
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) = cot-1x and f2(x) = x2,
Taking (1+x2)=a,
2xdx=da i.e. xdx=da/2
Again, x2=a-1
Replacing the value of a, we get,
The total integration yields as
, where c is the integrating constant