Evaluate the following integrals:

∫ 2x sec3 (x2 + 3) tan (x2 + 3) dx

sec3 (x2 + 3) can be written as sec2 (x2 + 3). sec (x2 + 3)


Now the question becomes



Assume sec (x2 + 3) = t


d(sec (x2 + 3)) = dt


2x sec (x2 + 3) tan (x2 + 3)dx = dt


Substituting t and dt in the given equation




.


39