Question #f3bd9
1 Answer
Explanation:
First, we can use the difference of squares formula:
Applying this to the numerator, we get:
Next we can use the Pythagorean identity to turn
Now we can split the fraction into two:
I will call the left one Integral 1 and the right one Integral 2
Integral 1
We can use the following identity to rewrite the integral:
We can now introduce a quick u-substitution with
This is the familiar derivative of
Integral 2
We can first use the following identity to rewrite the integral in terms of
We can now use this identity to rewrite the integral:
This gives:
We already worked out the left part in Integral 1, and the right part is just equal to
Completing the original integral
Now that we know Integral 1 and Integral 2, we can plug them into our original integral to get the final answer: