Integration using Trig identities

The goal is to convert the multiplication of terms to be addition of simple terms.

▶ Cheatsheet on previous note: Basic Integral Rules ▶ Cheatsheet on previous note:Basic Differential Rules ▶ Cheatsheet on previous note: All trig identities ▶ Back to previous note on: U-substitution → Chain Rule

Refer to Khan academy: Integrating using trigonometric identities

Example

Solve:

• We can identify there's a Integral trig rule we can apply on this problem:

  

• Therefore we're gonna organize it a bit with u-substitution and get the answer:

  

Example

Solve:

• This integrand has an odd power of sin(x), so we're gonna leave sin(x) alone and make an even power for sin(x), then make u-substitution upon it:

  

• And also we need to change the boundaries for the integral:

  

• Now we can start to integrate:

  

Example

Solve:

• We're gonna use a trig-integral-rule and a trig identity:

  
• Then apply them: