Integrals of the form sin(ax+b), cos(ax+b), sec² (ax+b) types

In this video, I show you how to integrate functions of the form sin (ax+b), cos (ax+b), and sec² (ax+b).

Formulae to remember:

  • \int{\sin (ax + b)} \text{ } dx = - \frac{1}{a} \cos (ax + b) + c
  • \int{\cos (ax + b)} \text{ } dx = \frac{1}{a} \sin (ax + b) + c
  • \int{\sec^2 (ax + b)} \text{ } dx = \frac{1}{a} \tan (ax + b) + c
  • \text{where } c \text{ is a constant.}

I show you how to integrate the following:

  1.     \[\int {{\textstyle{3 \over 4}}} \sin (5x - 2){\rm{ }}dx\]

  2.     \[\int {\frac{{4{{\sec }^2}(2 - 3x)}}{5}} {\rm{ }}dx\]

  3.     \[\int {\frac{3}{{\sec (2x)}}{\rm{ }}dx} \]

then to try these in the video:

  1.     \[5\int {\cos (4x - 7){\rm{ }}dx} \]

  2.     \[\int {\frac{{2\sin (3 - 8x)}}{7}dx} \]

  3.     \[\int {\frac{3}{{{{\cos }^2}(2x - 5)}}{\rm{ }}dx} \]




2018-08-09T07:36:00+00:00
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