Integrate e^(-x) Sin^(n) x. Hello friends, today I’ll show how to integrate e^(-x) Sin^(n) x. Have a look!!

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**Reduction formula for algebraic functions**

**Example 1 – Integrate e^(-x) Sin^(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

(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

So the integration of will be

Also, I already know that

So the integration of will be

Then I’ll simplify it to get

Since

Thus the value of will be

**Step 3**

(2)

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!!

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