We can take the integral of trig functions easily if we know the derivative of these trig functions.
Derivative of Trig Functions: • Derivative Part 3 - Derivative of Trig Fun...
If you want a review of trig functions and the unit circle take a look at these video:
Unit Circle: • Trigonometry Part 3 - Unit Circle Angles (...
Sine and Cosine: • Trigonometry Part 4 - Sine and Cosine
Tangent: • Trigonometry Part 6 - The Tangent Function
Secant, Cosecant, and Contangent: • Trigonometry Part 8 - csc sec cot