Science:Math Exam Resources/Courses/MATH101/April 2011/Question 04 (a)/Solution 1
Set the following change of variable
then we have
and so
Making this substitution in the integral gives
Now we use the method of partial fractions. We have
We want to find numbers and such that
Multiplying both sides by yields
Equating coefficients of powers of on both sides gives
From the first of these equations we see that . So the second equation becomes
Hence and . Therefore, we have
Using this to rewrite the last integral above, we find