Science:Math Exam Resources/Courses/MATH101/April 2005/Question 03 (c)/Solution 1

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We want to integrate:

The first step is to complete the square in the denominator:

Now we substitute:

So the integral simplifies to

We now perform a trigonometric substitution (this step is only valid for |y| smaller than 1, which we know is true because 1-y^2 must be positive):

So the above integral becomes:

But for any u, we have

So the above quantity is equal to

So we have


This is not required in a test, but we can check our answer by differentiating: