Integrate dz/(z^2 – a^2). Today I’ll show how to integrate an expression with the form dz/(z^2 – a^2). Have a look!!

**Integrate dz/(z^2 – a^2)**

Let’s suppose I have to integrate an expression like .

As I can see, I can get a partial fraction of . So it will be

You can read more about the technique at Partial fractions of lower degree numerators.

Next, I’ll find out the values of and . So I’ll simplify the right-hand side of the expression.

And that gives

Next, I’ll separate the coefficients. So it will be

As I can see, the bottom (denominator) is the same on both sides. So I can compare the top (numerator) now.

If I compare the coefficient of on both sides, I get

So this gives

If I compare the constants on both sides, I get

Since, , I can say that

So that gives

Therefore the value of will be

Thus the partial fraction of is .

So I can say that

Now I’ll integrate it. Therefore it will be

Since , I can say that

Now I’ll give you some examples of this technique.

**Solved examples of how to integrate dz/(z^2 – a^2)**

Disclaimer: None of these examples are mine. I have chosen these from some book or books. I have also given the due reference at the end of the post.

So here is the first example.

**Example 1**

According to Stroud and Booth (2013)*, “Evaluate the following:

”

**Solution**

Now here I have to evaluate the expression, say as

First of all, I’ll write it in the form of

So will be

Thus it will be

Next, I’ll simplify it. So that gives

Therefore I can say

Now I’ll integrate . Also, I’ll use the formula that I’ve mentioned above.

So it will be

And here is the integration constant.

Next, I’ll simplify it to get the value of as

Hence I can conclude that this is the answer to the given example.

Now I’ll give you another example.

**Example 2**

According to Stroud and Booth (2013)*, “Evaluate the following:

”

**Solution**

Now here I have to evaluate the expression, say as

First of all, I’ll write it in the form of

So will be

Thus it will be

Next, I’ll simplify it. So that gives

Therefore I can say

Now I’ll integrate . Also, I’ll use the formula that I’ve used in example 1.

So it will be

And here is the integration constant.

Next, I’ll simplify it to get the value of as

Hence I can conclude that this is the answer to the given example.

Now I’ll give you another example.

**Example 3**

According to Stroud and Booth (2013)*, “Evaluate the following:

”

**Solution**

Now here I have to evaluate the expression, say as

First of all, I’ll write it in the form of

**Step 1**

So will be

Thus it will be

Next, I’ll simplify it. So that gives

Therefore I can say

Now I’ll integrate . Also, I’ll use the formula that I’ve used in examples 1 and 2.

So it will be

And here is the integration constant.

Hence I can conclude that this is the answer to the given example.

Dear friends, this is the end of today’s post. Thank you very much for reading this. Please let me know how you feel about it. Soon I will be back again with a new post. Till then, bye, bye!!

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