Integration by Partial Fractions – Definition, Formula, Examples
Integration
Integration is a basic tool of mathematics that is used everywhere from physics to engineering. One of the questions in integral calculus that we find difficult and lengthy to solve is the partial fraction question. So below I will tell you a trick by which you will be able to solve partial fraction questions in one step!! This trick is very helpful to students giving SAT or other entrance test examinations.
The General Method
By using the general method you solve it by taking x equal to the factor and then putting it in the equation which gives you the numerator doing this to all factors and then applying the integration you get the result which is the difficult and lengthy way.
This is a part of the long way that is generally used this method covers at least 3 A4 pages for a small question and many pages for a lengthy one
The thing which must be kept in mind whether doing it by trick or general method the fraction should be proper that the numerator power must be less than the denominator power otherwise you have to make it proper by long division method,
The Trick Explained
For this trick, the question should have factors below it, if it does not you should make it into factors before applying this one-step trick.
These are necessary steps for every partial fractions question. This trick solves only those questions which have factors below them.
Now let’s take a simple question with factors below it and solve it in one step!
You have to first write ln, then solve the factor x=3 and x=-2 to get the coefficients for both factors which are here 1 and 2 for both, and then make a + sign between them as you can see in the image below:
This is how to do partial fraction questions in one step. If this helped you please like and share it for more tricks like this in the future, Thanks
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