In this tutorial you are shown how to do integrals of the above form using these examples

  1.     \[\int {\frac{3}{{5x}}{\rm{ }}dx} \]

  2.     \[\int {\frac{5}{{3x - 2}}{\rm{ }}dx} \]

Formulae to remember:

  • \displaystyle\int{\dfrac{1}{x}} dx = \ln {|x|} + c
  • \displaystyle\int{\dfrac{1}{(ax + b)}} dx = \dfrac{1}{a} \ln {|(ax + b)|} + c

Then asked to try the following:

  1.     \[\int {\frac{7}{x}{\rm{ }}dx} \]

  2.     \[\int {\frac{6}{{7x}}{\rm{ }}dx} \]

  3.     \[\int {\frac{2}{{3x - 1}}{\rm{ }}dx} \]

  4.     \[\int {\frac{3}{{5\left( {2x - 7} \right)}}{\rm{ }}dx} \]