Integrate e^(-x) cos^(n) x. Hello friends, today I’ll show how to integrate e^(-x) cos^(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****Integrate Cot^(n) x dx | Reduction formula for Cot^(n) x****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 e^(-x) cos^(n) x**

**Example 1 – Integrate e^(-x) cos^(n) x**

So now I’ll integrate . Therefore I’ll give it a name, say, . So I say,

Also, it has another name. And that is the reduction formula for .

**Step 1**

Now I’ll use the * integration by parts* method. And that says

So in this case, I’ll choose as and as . If , then If , then

Thus becomes

So this means

(1)

Now I’ll integrate .

**Step 2**

Again I’ll use the ‘integration by parts’ method. And for that, I’ll choose as and as . If , then If , then I’ll use the * product rule of differentiation* to get the value of .

Thus it will be

Now I’ll simplify it to get

Also, I already know that

Therefore the value of will be

If I simplify it, I’ll get

So this means

Thus the integration of will be

Then I’ll simplify it to get

Also, I can rewrite it as

Since

(2)

**Step 3**

Now I’ll substitute equation (2) to equation (1) to get

Next I’ll simplify it. And that gives

So this means

Thus the value of will be

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!!

## Leave a Reply