1. ## Intergrating Trignometric Functions:revisting

This is my second post.In my first one I asked about the integration of trig functions which have a domain other than x only.From the answer I concluded that first you have to take the derivative of the domain then multiply the inverse of that derivative with the integral of the trig function,keeping its domain unchanged.
My question is that does it only work if in the domain x has power 1 or it is also valid for higher powers of x and for exponential expressions in the domain.

2. ## Re: Intergrating Trignometric Functions:revisting

Originally Posted by reindeer7
This is my second post.In my first one I asked about the integration of trig functions which have a domain other than x only.From the answer I concluded that first you have to take the derivative of the domain then multiply the inverse of that derivative with the integral of the trig function,keeping its domain unchanged.
My question is that does it only work if in the domain x has power 1 or it is also valid for higher powers of x and for exponential expressions in the domain.
I for one find your question very hard to follow.
You should take a look at this webpage.

As you can see $\displaystyle \int {\cos ({x^2})dx}$ is very hard to do. In fact it requires a very special function.

Whereas $\displaystyle \int {x\cos ({x^2})dx}=\tfrac{1}{2}\sin(x^2)+C$ is very easy.

You can use that webpage and change the question by adding the x factor and clicking $\displaystyle \boxed{=}$.

3. ## Re: Intergrating Trignometric Functions:revisting

Error- I mis-read this as "derivative".

4. ## Re: Intergrating Trignometric Functions:revisting

what did you mean by this