INTEGRATING PRODUCTS OF TANGENTS AND SECANTS
Consider the following integral :
Case 1 :
If q is a positive even positive integer, substitute
u = tanθ
and evaluate the integral by substitution method.
Case 2 :
If both p and q are positive odd integers, substitute
u = secθ
and evaluate the integral by substitution method.
You may have to use the following trigonometric identies.
sec2θ = 1 + tan2θ
tan2θ = sec2θ - 1
Evaluate each of the following integrals.
Example 1 :
Solution :
Let u = tanθ.
ᵈᵘ⁄dθ = sec2θ
du = sec2θdθ
Example 2 :
Solution :
Let u = tanθ.
ᵈᵘ⁄dθ = sec2θ
du = sec2θdθ
Example 3 :
Solution :
Let u = secθ.
ᵈᵘ⁄dθ = secθtanθ
du = secθtanθdθ
Example 4 :
Solution :
Let u = secθ.
ᵈᵘ⁄dθ = secθtanθ
du = secθtanθdθ
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