Partial fraction is a technique that reduces the power of the original denominator to give separate fractions. These separate fractions are then being added with a denominator of a lower power, which is much easier to integrate. By making the correct choice for the numerator then the partial fractions will lead to answers of natural log or arctan.
This video will help you to choose your decompositions and numerators.
Example Problems covered in this series
1. Integral [ 1 / (x^2 + 6x + 8) dx ]
2. Integral [ 4 / (x^2 + 6x -7) dx ]
3. Integral [ 2 + x / (x^2 + 5x) dx ]
4. Integral [ x + 5 / (x^3 + 2x^2 + x) dx ]
5a. Integral [ -4x / (-2x -15) dx ]
5b. Integral [ (3x^2 + 45) / (x^2 + 45x + 105) dx ]
6. Integral [ (4x^2 + 5x +18) / (x^3 - 6x^2 + 9x) dx ]
7. Integral [ 1 / (9x^4 - 25x) dx ]
8. Integral [ (36x^3 - 18x - 54) / (x^2 - 3x )( x^2 + 9) dx ]
9. Integral [ 9x^3 + 37x / (x^2 + 5)^2 dx ]
10. Integral [ 12x^3 + 5x / (x^2 + 1)^2 dx ]