How to integrate dx/(a cos^2x+bsin^2x+c). Here I show how to integrate Have a look!!

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

integrate_1_compressed

**Integrate dx/(a cos^2x+bsin^2x+c)**

Now I’ll integrate

So let’s say . Then will be

And will be

If I differentiate , I get

So this means

Since , will be

Thus will be

Then I’ll simplify it to get

Since , I can say that

And then I can integrate it accordingly.

Now I’ll give you some examples of that.

**Solved examples of how to integrate dx/(a cos^2x+bsin^2x+c)**

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 replace with as I have mentioned above.

So let’s say . Then will be

And will be

If I differentiate , I get

So this means

Since , will be

Thus will be

Then I’ll simplify it to get

Since , I can say that

Next, I’ll take out from as

As I can see, I can use the same method as the **integration of **. So that gives

And is the integration constant.

Now I’ll simplify it to get

Then I’ll replace with to get

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 replace with as I have mentioned above.

So let’s say . Then will be

And will be

If I differentiate , I get

So this means

Since , will be

Thus will be

Then I’ll simplify it to get

Since , I can say that

Next, I’ll take out from as

Then I’ll use the same method as in Example 1. So that gives

And is the integration constant.

Now I’ll simplify it to get

Then I’ll replace with to get

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 replace with as I have mentioned above.

So let’s say . Then will be

And will be

If I differentiate , I get

So this means

Since , will be

Thus will be

Then I’ll simplify it to get

Since , I can say that

Next, I’ll take out from as

As I can see, I’ll use the same method as the * integration of *. So here it will be

And is the integration constant.

Now I’ll simplify it to get

Then I’ll replace with to get

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!!

## Leave a Reply