Integration by Trigonometric Method (tangent secant)

Integration by Trigonometric Method (sine cosine) has been discussed in the previous entry. In this entry, we will discuss about trigonometric method when the integrand, f (x)  is a product of  tan x and sec x.

How to evaluate  ∫ tanm x secn x dx   ?

1.) Power of sec is even : n = even no.(and m = even no.)

• Split off a factor of sec2 x
• Use identity, substitute sec2 x = 1 + tan2 x
• Let u = tan x

eeeeeeExamples:  ∫ tan6 x sec4 x dx

2.) Power of tan is odd : n = odd no. (and m = odd no.)

• Split off a factor of sec x tan x
• Use identity, substitute tan2 x = sec2 x -1
• Let u = sec x

eeeeeeExamples:  ∫ tan5 x sec9 x dx

3.) If power of sec is even and power of tan is odd

• Use either method (1) or (2) but it is easier to convert the term with the smallest power.

eeeeeeExamples:  ∫ tan3 x sec4 x dx

Click here for examples.

Here's  more:

Integration by Trigonometric Method (sine cosine)

Examples of Integration by Trigonometric Method (sine cosine)