Integral of sec of a quadratic factor * tan of the same factor:

If the correct factors are present, this can be handled by the integral resulting in the secant:

, where ; . Hence a combination of factors in the original problem can be replaced:

With this substitution, we get

Finally, we substitute for u to get the result in terms of x:

Notice that the argument of the resulting trig function is the same as that in the original problem.