I know I need to use substitution and I am aware of the fact that = derivative of arcsin(x), but I am unsure how I apply these to the above problem.

I have the answer but I don't follow the steps to get to it.

Printable View

- Oct 20th 2011, 11:51 PMterrorsquidarctan/arcsin and integration by substitution

I know I need to use substitution and I am aware of the fact that = derivative of arcsin(x), but I am unsure how I apply these to the above problem.

I have the answer but I don't follow the steps to get to it. - Oct 21st 2011, 12:26 AMQuackyRe: arctan/arcsin and integration by substitution
Let

We can do it by substitution, but I wouldn't personally. However, it's good to start from there.

So I'm going to let

This means that so

Factoring the :

Applying for :

But as ,

So

Now, I let right at the start of my substitution. This means that , so

Giving us the required final answer of

Is this clear? Usually I'd ask you to do part of the problem yourself but I don't think there's really a good place to stop with this question. - Oct 21st 2011, 01:47 AMsalimRe: arctan/arcsin and integration by substitution
hi,

the problem is easy

let y=x/9 => x = 9y and dx = 9dy

then

the solution is : arcsin(y) + c

i.e. arcsin(x/9) + c