Q. 424.0( 4 Votes )

Evaluate the following integrals:



[CBSE 2006C]

Answer :

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


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