Example 6:
INTEGRALS OF TRIG FUNCTIONS
The integrals of some trigonometric functions follow directly from the derivative formulas in Chapter 6.
∫ sin ax dx = − + C
∫ cos ax dx = + C
∫ sec ax tan ax dx = + C
∫ sec
(^2) ax dx = + C
∫ csc ax cot ax dx = − + C
∫ csc
(^2) ax dx = − + C
We didn’t mention the integrals of tangent, cotangent, secant, and cosecant, because you need to know
some rules about logarithms to figure them out. We’ll get to them in a few chapters. Notice also that each
of the answers is divided by a constant. This is to account for the Chain Rule. Let’s do some examples.
Example 7: Check the integral ∫ sin 5x dx = − + C by differentiating the answer.
(−sin 5x)(5) = sin 5xNotice how the constant is accounted for in the answer?
Example 8: (^) ∫ sec^2 3 x dx = + C