INTEGRATION OF TRIGONOMETRIC FUNCTIONS

Compute each of the following integrals.

Problem 1 :

∫ sin x dx

Solution :

Given, ∫ sin x dx

= -cos x + C 

Problem 2 :

∫ cos 5x dx

Solution :

Given, ∫ cos 5x dx

Let u = 5x, du = 5 dx

dx = 1/5 du

Problem 3 :

∫ cos x sin⁴x dx

Solution :

Given, ∫ cos x sin⁴x dx

u = sin x, du = cos x dx

= ∫ u⁴ du

= u⁵/5 + C

= (1/5) sin⁵x + C

Problem 4 :

∫ csc² x dx

Solution :

Given, ∫ csc² x dx

= -cot x + C 

Problem 5 :

∫ tan x dx

Solution :

Problem 6 :

∫ cot x dx

Solution :

Problem 7 :

∫ sec x dx

Solution :

Problem 8 :

∫ csc x dx

Solution :

Problem 9 :

Solution :

Problem 10 :

Solution :

Problem 11 :

Solution :

Problem 12 :

Solution :

Problem 13 :

Solution :