Thank you again but now im sort of getting embarassed because I never learnt any partial fractions, so even though I looked at series of websites, that explains partial fraction, I still can't apply it... I know it's really annoying, but could you help me just a little bit more???
You begin by assuming the integrand may be expressed in the form:
Now multiply through by the lowest common denominator
Now, expand the right side and arrange as a quadratic in standard form, and write the left side as:
Then equate corresponding coefficients to arrive at a linear 3X3 system in A, B, and C for which there is a unique solution.
Thank you for your help once again, but would it be asking too much if I ask you to solve this problem (the second one) for me? I know you are only meant to give directions and helps but I have a very limited knowledge about partial fractions. Also, I have like 5 of questions that look similar but with completely different numbers, and other 10-15 questions completely different. So could you please do me a favour just once?
Totally understood. What I have done so far is from your advice and MarkFL2's advice. what I have got is
1=36Au^2+12Au+A+6Bu^2+Bu+Cu
which is basically an expansion of 1=A(6u+1)^2+Bu(6u+1)+Cu.
I have no idea how to go from here..
You have two of the values correct. Did you try substituting the solutions into the equations to make sure all 3 equations are satisfied?
Once you have the correct solutions, then you may put their values into:
to get the partial fraction decomposition of the original integral. You will then have 3 terms which you can easily integrate.