Evaluate the following integrals:


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


1