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