Integration of dz/(z^2+a^2). Hello friends, today I’ll talk about the integration of . Have a look!!

Want to know more about the integration of different forms of expressions? Check these out:

integrate_4_compressed

**Integration of dz/(z^2+a^2) **

Let’s say I have an expression of the form . And I have to integrate it. So the question is: how to do it?

Ok, now I choose . So is

Then I’ll simplify it. And that gives

Since , I can say that

Also,

Therefore the expression in terms of becomes

Since , I can say that

Then I’ll integrate it to get

Since . I can say that . And that gives

Thus the integration of is

Now I’ll give you some examples on that.

**Solved examples on the integration of dz/(z^2+a^2) **

Disclaimer: Some of these examples are mine but others are not. I have chosen these other ones 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 take out as a common factor from that botttom. So that gives

Next, I’ll simplify it to get

Then I’ll bring term at the bottom. And that means

Now I’ll simplify it to get

Therefore I can rewrite it in the form of as

Since the integration of is , I can say that the value of will be

Next, I’ll simplify it. And that becomes

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 bring term at the bottom. And that means

Next, I’ll simplify it to get

Therefore I can rewrite it in the form of as

Since the integration of is , I can say that the value of will be

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

Now I’ll give you two more of my self-made examples.

**Example 3**

Find out the value of

**Solution**

Now here I have to evaluate the expression, say as

First of all, I’ll bring term at the bottom. And that means

Since the integration of is , I can say that the value of will be

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

Now I’ll give you one more example.

**Example 4**

Find out the value of

**Solution**

Now here I have to evaluate the expression, say as

First of all, I’ll bring term at the bottom. And that means

Next, I’ll simplify it to get

Therefore I can rewrite it in the form of as

Thus the value of will be

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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