In this video I show you how to integrate types like this as seen in the examples below.

Although I give you a formula, it is important that you understand the chain rule to fully appreciate the concept rather than rely on the formula.

Formulae: Try and understand how it works rather than learn it.

  • \displaystyle\int{(ax + b)^n dx} = \dfrac{1}{a(n+1)}(ax +b)^{n+1} + c

Examples: Evaluate the following

  1. \displaystyle\int {(3x + 2)^4} dx
  2. \displaystyle\int {\dfrac{7}{(5x - 1)^3}} dx
  3. \displaystyle\int {4 \sqrt{7x - 3}} dx

Summary Exercise

Examples:

  1. \displaystyle\int {2(10x + 3)^2} dx
  2. \displaystyle\int {7\sqrt[3]{{{{(2x - 4)}^2}}}} dx
  3. \displaystyle\int {\dfrac{5}{{{{(7x + 1)}^4}}}} {\rm{ }}dx