Integrate Cot^n (x). Hello friends, today I’ll talk about how to integrate Cot^n (x). Have a look!!

Want to know more about the reduction formulas of other functions?? Have a look at the followings:

**Reduction formulas for trigonometric functions**

**Reduction formula for Sin^(n) x | Integrate Sin^(n) x dx****Get the reduction formula for Cos^(n) x | Integrate Cos^(n) x dx****Reduction formula for Tan^(n) x | Integrate Tan^(n) x dx****Reduction formula for Sec^(n) x | Integrate Sec^(n) x dx**

**Reduction formulas for logarithmic functions**

**Reduction formulas for hyperbolic functions**

**Reduction formulas for algebraic functions**

**DOWNLOAD, READ & PRINT – Integrate Cot^n (x)**

**Integrate Cot^n (x)**

**Solved example of how to i**ntegrate Cot^n (x)

Disclaimer: This example is not mine. I have chosen it from some book. I have also given the due reference at the end of the post.

So here is my example.

**Example **

According to Stroud and Booth (2013)*, “If , show that

Hence determine .”

**Solution**

Now here I have to integrate , that is,

Also I have to prove that

**Step 1**

First of all, I’ll write as

Also, from the * standard formulas in trigonometry*, I know that

Therefore will be

So will be

Then I’ll simplify it as

And that gives

Also, if , then

(1)

Now I’ll integrate .

**Step 2**

Since I already know that , I can rewrite as

Thus will be

If , then . Thus will be

Now I’ll integrate the right-hand side to get

Next, I’ll simplify it. And that gives

(2)

Now I’ll put back the equation (2) to equation (1) to get

(3)

Hence I have proved the relation. And this is the first part of the given example.

Next, I’ll get the value of .

**Step 3**

So I’ll substitute in equation (3) to get

(4)

Now I need the value of to get the value of . So I’ll substitute in equation (3) to get

Then I’ll simplify it and that gives me

(5)

Again I have to get the value of to know the value of . So I’ll put in equation (3) to get

After simplifying it, I get

(6)

Now equation (3) is only true for any value of greater than . So I’ll put in . Therefore I can say that

And this is because

Next, I’ll do the integration. So I can say that

where is the integration constant.

Thus my next step will be to get the values of and respectively.

**Step 4**

So I’ll put in equation (6) to get the value of as

Now I’ll simplify it to get

Next, I’ll put in equation (5) to get the value of as

Then I’ll simplify it and that gives

Now I’ll put in equation (4) to get the value of as

Next, I’ll simplify it.

So I can say that

where .

Hence I can conclude that this is the solution 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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