Integration – Terms of the form axn

Integration can be thought of as the inverse of differentiation.

In the initial video I introduce you to this concept and explain the notation used and run through how we apply the following formulae.

Formulae to remember:

  •     \[{\int {{x^n}dx}  = \frac{{{x^{n + 1}}}}{{n + 1}} + c}\]

  •      \begin{align*} \int {a{x^n}dx} &= a\int {{x^n}dx} \\ &= \frac{{a{x^{n + 1}}}}{{n + 1}} + c \end{align*}

  •     \[{\int {a{\rm{ }}dx}  = ax + c}\]

Fractional and root type terms

Integrals that contain one term where x is in the denominator can often be rearranged and then integrated. In the video that follows I show you how to do the following.

Examples in the video

  1. \displaystyle\int {\dfrac{4}{{{x^2}}}dx}
  2. \displaystyle\int {\dfrac{5}{{4\sqrt[3]{{{x^2}}}}}} dx