The integral is .

(a)

 is positive and even.

If the power of a secant function is positive and even, save a secant squared factor and convert the remaining factors to tangents.Then expand and integrate.

(b)

 is positive and odd.

If the power of a tangent function is positive and odd, save a secant tangent factor and convert the remaining factors to secants.Then expand and integrate.

(c)

 is positive and even and there are no secant factors.

If there are no secant factors and the power of a tangent function is positive and even, convert a tangent factor to a secant squared factor,then expand and repeat if necessary.

(d)

 is positive and odd and there are no tangent factors.

If the integral is of the form  , where  is odd and positive, use integration by parts.

(a) If the power of a secant function is positive and even, save a secant squared factor and convert the remaining factors to tangents.Then expand and integrate.

(b) If the power of a tangent function is positive and odd, save a secant tangent factor and convert the remaining factors to secants.Then expand and integrate.

(c) If there are no secant factors and the power of a tangent function is positive and even, convert a tangent factor to a secant squared factor,then expand and repeat if necessary.

(d) If the integral is of the form  , where  is odd and positive, use integration by parts.