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

< Science:Math Exam Resources | Courses/MATH101 | April 2005 | Question 03 (c)(Redirected from Science:Math Exam Resources/Courses/MATH101/April 2005/Question 3 (c)/Solution 1)

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:*