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

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

**How to integrate √(a^2 – x^2) dx**

**How to integrate d z/√(z^2-a^2)**

**Integration of d x/√(x^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

So becomes .

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

Thus the integration of is

Now I’ll give you some examples of that.

**Solved examples of the integration of d x/√(x^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 are the examples.

**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

Next, I’ll rewrite it as

Then I’ll simplify it. So it becomes

Now I’ll integrate . Also, I’ll use the formula that I’ve mentioned above. So it will be

where is the integration constant.

Next, I’ll simplify it to get

So this means

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

Now I’ll integrate . Also, I’ll use the formula that I’ve mentioned above. So it will be

where 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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